If some of the other answers don't let you figure out the root of the problem and get him more involved in the non-roleplay segments, that's fine. Roll with it. As long as he has a sense of humour it'll be fine. I've shared a table with many an odd duck, and if they don't fit the game, but you want to keep them around, then you fit the game to them. Otherwise you might as well be playing DnD Online. So from your description, here's what I'd do based on past experience with similar (but not quite as difficult) players:

What you've got here is a stereotypical absent-minded wizard, only in sorcerer form. Just pretend he's role-playing through the middle of combat too. Potentially you might even encourage him to do exactly that since it seems to be his preferred mode of operation. Absent-minded wizards are usually NPCs, but that's not a hard requirement. Shift some of the things you might be tempted to reveal via an absent-minded wizard onto him. Tell them to him privately, with no repeats, and make him write them down himself. His horrible note-taking will play right into your hands. The frustration of knowing that he should know this critical piece of plot-relevant information will encourage him to start taking better notes.

He casts a spell and doesn't know what it does? That's fine, he's a sorcerer and brings magical effects into being by force of personality. If he's not focused enough to shape the forces he's channelling, then you get to just make something up. "Magic missal" sounds like it summons a prayer book for the cleric. "Meatier Swarm" sounds like the enemy is about to get pelted with steaks for a few d6 worth of damage. "Feather Fall" sounds like the party will be able to re-stuff their pillows and bedrolls once they dig themselves out of the pile at the bottom of the cliff. "Mold Earth" and "Burning Hands" could have nasty side-effects... Especially near steaks or feathers.

Don't explicitly tell him the combat's over. If he wants to keep shooting at things that are already dead, that's fine. People sometimes do this in real life too.

He can't come up with one of his stats within 20 seconds? That's fine, he's obviously too distracted to really be attempting the check anyway, so make up a number for him, say by rolling some number of dice (probably 1-3d6 depending on what you're replacing.) Don't tell him what it is, just have him roll the d20. Insert improbable explanations for successes or failures near the edges of the bell curve.

His talent for roleplay gets to be useful to the group. His ineptitude in combat gets to be entertaining, without dragging things out to the point where the delay becomes frustrating. In a group as large as yours it's ok to have a couple of characters who aren't combat-oriented. Have the cleric take charge of plunking him down somewhere with good cover at the beginning of a fight so he can shoot his crossbow one-handed over a rock without looking and hope for the best. If he's really into role-play then getting him to play a character in a fight, not just a collection of numbers looking for optimal paths to kill things may well be your last hope of getting him more involved, and a panic-prone, absent-minded magician fits what he's already doing, so it would be a good starting point. He can develop the character further as the plot thickens.

Guide him to a simpler class, or lay down the law

It sounds like your problem-player has a lot of faults: he is disorganized, forgetful, and not really invested in learning the rules of this game. But it also sounds like he has a lot of strengths: he is great at role playing, and genuinely invested in the group's progress (I'm guessing based on their out-of-combat use of spells).

The good news is that DnD can accommodate all kinds of play-styles, from all kinds of players. There are classes which are designed to be playable by extremely detail oriented people, with a good sense of mathematics and a good memory for minutia. And then there are classes for people who are looking for fewer rules to remember, and a simpler but equally effective strategies. It sounds like your player is one of the latter.

You did exactly what you should have done in the first place: "told him... he'd probably have more fun playing a non-magic class but he insisted." That was the right call: many classes, like the Champion Fighter class, are designed to be very rules light, but very effective. It sounds like you tried to suggest they play one, but it didn't work. The way I see it, you have three main options:

1.) Suggest a non-caster class again (now that he's tried magic)

The player didn't want a non-caster class: they wanted a sorcerer. But maybe now that they've played one for a while, they might change their mind. They've seen how hard it can be to keep track of all the little details of spells and spell slots (not to mention sorcery metamagic, or other details). Now that he knows he has to do this on top of keeping track of hit points and other details, he might be persuaded to try another simpler class.

2.) Find out WHY he wants to be a sorcerer

Your player insisted on playing a magical class: my main question is "why?" Did they think the role in the party sounded appealing, or did they like the backstory options that the class gives them, or did they want some specific ability that Sorcerers have, or what?

The answer to this question might help you direct them towards a simpler character type. What if they wanted to be a sorcerer just because it sounded cool to be a descendant of an ancient dragon? That's something they can do with any class (though it wouldn't usually have a mechanical benefit). What if they wanted to be a sorcerer just because they wanted to be able to cast a particular spell, like invisibility? Then you could direct them towards simpler stealthy classes, or give him a magic item that lets him cast that one particular spell a few times a day as a fighter. Or like Daniel Zastoupil suggested you could direct him towards the Warlock class: a spellcaster, but one with considerably fewer decisions to make, as they can only cast a couple of spells per combat.

But maybe none of that works: maybe he really likes his character concept and doesn't want to start a new one. Maybe the things he wants his character to be able to do is to fill a role in the party that a sorcerer fits, but simpler classes do not. In that case, I have a third suggestion:

3.) Restrict him to spells he understands/has written out

This player keeps forgetting to bring printed descriptions of spells, or study the rules. That is 100% their responsibility, and no one is required to do this for them. But part of the reason they may keep forgetting is that there are currently few repercussions to them for not knowing the rules: someone else will help them, whether it's you or another player. If you want this behavior to change, then there needs to be some consequence of the player being unprepared.

Minha sugestão: declare that if he doesn't know what a spell does, his character forgets that too, and he can't cast it.

This is a rare case where a player's growth and their character's growth can go hand in hand. It's not only a reasonable reaction to a player who repeatedly has forgotten to learn the rules, it's a reasonable possibility for something his character may face. First of all, a Sorcerer's powers aren't gained through research and study like a Wizard's: they're inborn and natural. So a sorcerer may not always exactly know what they can and can't do. Most will, as they'll devote serious time and effort to learning their own limits and potential. But some might simply keep trying something blindly, and hope it works. If your player insists on not learning their characters' abilities, then maybe their character does the same thing.

Second of all, combat can be a wild and chaotic time (both in and out of character). Your player and their character may simply forget what they can do in the heat of battle, or become flustered and uncertain. If that is happening, make it part of the story: the character is a source of great power, but they are too scatterbrained in combat to use it effectively: at least, so far.

This will mean that once your player actually prints out the spells and has them in front of him, the character has also been putting effort into learning and paying attention to their abilities, and is more capable of bringing their might to bear in combat. It will actually become part of the story: not something frustrating to be mad about but something exciting to watch.

It sounds like your player is much more invested in their character as a person than as a series of stats. So tie the player's understanding of the stats into the character's personality. If they want to play a person who is useless under pressure and can barely remember the power they have inside them, let them. But if they want their character to grow and change, to have an arc that shows development and meaningful progress, they'll have to show some progress themselves.

Change his class

If keeping track of spells is the issue, but he's overall a fun player, an efficient way of resolving this problem is to get him a class that he'll feel comfortable with. The Sorcerer has a lot of options to choose from, especially once you throw Metamagic into the mix.

But you know who não have a lot of decisions? Feiticeiros. They are probably the easiest spellcaster in the world once you decipher how their spell slots work.

• Want him to shine out of combat? Boom, disguise self as a cantrip at level 2.

• Want him to track his own spells, but he's as oblivious as a lemming? Boom, Eldritch Blast. Most boring, easy spell to track, and the only damage spell he'll need. Later on, he could invest in Hex, but I'd suggest he take it slow for now.

• Want him to track his spell slots? Boom, Warlock Spells only have 1 spell slot level to track for all of their spells.

• Want him to add even amoras out of combat? Boom, Pact of the chain. Give that guy a sarcastic familiar, and watch this guy do wonders for your game.

The playstyles between warlocks and sorcerers aren't that different; you don't even need to update his stats. Just say he encountered a spirit that wished to become his friend, and he "accidentally" became bonded to it, making him a warlock bonded to a higher being, with the spirit as his "contact" (now acting as his familiar). Since he didn't have much control over his magic before, his patron refined it and now all of his levels were rewritten to be Warlock levels.

You can find a million+1 posts about people having problem players, and tons of paragraphs of information on how to educate people into being smart or polite, but this is going to be the easiest solution that doesn't require a PHD in Psychology and utilizes the system to both of your benefit.

This appears to be a case of overcasualitis. I've encountered this a few times, where players simply want to be part of a game where they can do cool things but the mechanics are simply a hindrance to them having a good time (the all fun, no effort mentality).

There are a few ways of dealing with this, but first a bit of friendly advice: the good of many outweighs the good of the few. If none of the solutions you try out work, then talk to the rest of the group. If they say that this is really ruining their enjoyment of the game, then removing him from the group may ultimately be your best option, especially since he seems to outright refuse to correct his bad habits. That said, here are some alternative:

1. Talk to him friend-to-friend out of game. If he's truly your friend, as you seem to suggest, then sit him down and explain to him that his approach is also hurting seus enjoyment of the game, in which you are a player (albeit with a different role than the others). You are just as entitled to having fun as he is, after all. If he doesn't care, or say that as the DM your job is to carry the players along, then you have problems beyond him being spacey.
2. Have him change his class. While this might seem harsh, explain to him that if he refuses to play his class, then he must choose one that he will be willing to play fully. Others have suggested the Bruxo, which I agree is a great option due to their simplicity and the fact that most of their abilities recharge on a short rest, making keeping track of them a lot easier. Also, they have the best attack cantrip of the game, Eldritch Blast, which will help him out in-combat.
3. Have a one-on-one session with him. Run a simple combat encounter and take some time to make sure he understands the basic rules and gets a feel for his spells.
4. As a last resort, make him feel the consequences of his refusal to learn the rules. He doesn't know what his spell does? Then he fails in casting it. He doesn't protect himself in combat? Well if he drops unconscious don't metagame to spare his character. He forgets to write down xp or an item? Then he doesn't get it. If he forgets to mark off his spell slots, sorcery points or ammo, make a small sheet of his character for yourself and mark them down, and if he tries to use more than he has tell him he can't. This might seem harsh, but he's doing it to himself and he shouldn't get preferential treatment for refusing to learn the rules of a game he chose to play. That said, this really is a last resort, and that kind of action can ruin a relationship outside of game. I would recommend removing him from the game before doing this, or clearly explaining to him why you are doing it.

All in all some players can be detrimental to a positive atmosphere, and when they refuse to learn how to game is played despite others asking them to do so it shows a profound lack of respect towards the others. As the DM, you have a responsibility to the entire group, not just to a single player. If the situation doesn't improve, talk to the rest of the group to see what they think should be done. If they want to kick him out, then issue out a warning to him first, and if he blatantly ignores it then enact the will of the majority. Make sure that you are clear and tactful in why the group feels this way, so that he may learn from his mistakes and become a better player in the future.

Upon reading other answers, I've realized that his mentality might not be an uncaring one, but simply one where he is concerned about the advancement of the group in RP rather than in combat. Some players indeed play D&D solely for the social aspect and do not enjoy the mechanics, and in this case a compromise may be reached by several means, the best of which are covered by other answers and mix in elements of the real life actions of players with their character's RP.

I'd suggest getting him a character sheet app or spreadsheet, so the computer can keep track of all that instead of him having to do it. I used The Only Sheet for many years while playing 3.5e, and it was great at helping me remember things like spells, bonuses, etc. They also have a 5e version.

Have you thought about buying or making spell cards for him? I found them very useful when I first played a wizard. They have a nice tactility to them, I enjoyed looking through my deck of options. You shouldn't have to provide these yourself, but there you go, at least they might come in handy with future players!

You could also buddy him up with another player who commits to bringing his character sheet along as well as their own. I do this for our scatterbrained Druid and it cuts down on hastily remaking sheets.

Here is a passive solution I used.

I had a similar situation, where in my frustration I created a note sheet for them, with 2 QR codes. I had 2 PP in my party of 6 players. So I made the QR codes myself with a free app, pointing to an SRD site with one for the players class and one for the classes spells. As a point not to single them out, I made sheets for all my players with their class and class spells. As well as a sheet full of QR codes pointing to various parts of the SRD 5e site.

At first they didn't take to it. But after I kept reminding them the answer is in those QR codes. They started to use it and eventually stopped asking because they had the answers at their finger tips in the size of a single sheet of paper with 2 QR codes.

This was not overnight. It took a few games for it to stick, it was the middle of the 3rd game I noticed it working.

BTW...Only 1 person had to install a QR reader, everyone else had one on their phones or tablets already.

I would like to give another alternative option: make him a reference sheet for his spells and sorcery points. (This doesn’t address all of your concerns, but I think going this far is at least meeting the player halfway.)

I’ve had a Sorcerer player who wasn’t good with memory or rules comprehension, and I mean wasn’t as capable in those areas rather than that they didn’t care. Rather than penalise them I made reference sheets for everyone; useful because I was the only one who owned rulebooks, so it saved passing my PHB around, but also because the act of making the sheets helped me learn the capabilities of the group so I was better equipped to answer questions (my group were also mostly new players).

In your case you only need to do this for one player and since he’s a sorcerer the number of spells he’ll know is relatively small. It won’t take you much to make a reference sheet/cards for him (you can copy and paste from the basic rules for race and class features and most spells), or even to keep it updated at level up if he can’t manage that, and if he doesn’t refer to them then you’ll have your answer about whether this is an attitude or ability problem.

But take into account that part of the DM’s job is to make the game fun and to teach it to everyone, and while most players can handle their own stuff, some will need more of a helping hand. I don’t think assembling the official rules for players constitutes nannying, and nor does it oblige you to do so for everyone else; instead you’re giving him the tool he really needs to be self-sufficient, and if he’s also frustrating the other players they will be glad of the extra help you give him if it works. From each according to their ability, to each according to their need as the saying goes, and nothing in your post seems to preclude him genuinely being bad at the things you’d wish he’d do, as opposed to being wilfully annoying. Unless he is a deliberate troublemaker, the benefit of him having that reference at the table which you can prompt him to read when necessary will far outweigh the time and effort needed to make it - and either way, if you try this you’ll know. Hopefully if you explain the effort you’ve made it will also encourage him to make more of an effort with the other stuff as well.

One last alternate suggestion, again if he really has problems with understanding or keeping track of stats: surely there is a player at the table who is a gun at that stuff but not such a good role player. Get them to team up (as players if not characters) whenever possible, and hopefully they can learn from each other.

While there are a lot of answers here that are great, I would like to add a little something myself.

I do think that this player of yours might be

Not interested - He is there because maybe, as you're friend he supports your fun stuff, or it might be because of some peers of the group.

He has problems he cant share with you, but playing the game somehow "masks" his pain - He uses this session as a part of escape, his mind is not in the game, but somehow when he is with you, he forgets his problems, but could not put his mind off of it.

Talking to him is the real solution, as you have stated he is your friend, other answer here (including the ones that you have already marked as your answer) will help you pinpoint what the real problem is, who knows, maybe you'll end up with a fun player and helped him with his problem (if he has) Good luck!