tldr; Gimli e Frodo, juntos, perguntaram a Gandalf sobre suas memórias de eventos

Há 'The Quest of Erebor', onde Gandalf, em Minas Tirith, contava os acontecimentos de O Hobbit de sua perspectiva para Frodo, Pippin, Merry e Gimli. A linha de abertura em Contos Inacabados é:

He [Gandalf] would say no more that day. But later we [Frodo, Pippin, Merry and Gimli] brought the matter again, and he told us the whole strange story;

a identificação dos personagens está nas notas de Christopher Tolkien. Em uma versão anterior, Gimli é registrado como falando e comentando a história

"It still sounds absurd," he said, "even now that all has turned out more than well. I knew Thorin, of course; and I wish I had been there, but I was away at the time of your first visit to us. And I was not allowed to go on the quest: too young, they said, though at sixty-two I thought myself fit for anything. Well, I am glad to have heard the full tale.

Nesta versão, acho que Merry e Pippin estavam ausentes, com apenas Frodo e Gimli conversando com Gandalf.

Pode-se imaginar que fora da página houvesse alguma discussão entre Frodo e Gimli, pelo menos, no que eles acabaram de ouvir, ou mesmo discussão entre eles antes da história de Gandalf.

Nunca foi declarado explicitamente que Gimli e Frodo discutiram as aventuras, mas,

Glóin e Frodo certamente fizeram

Antes do Conselho de Elrond, após a recuperação de Frodo, Frodo e Glóin passam muito tempo discutindo as aventuras, bem como o futuro dos membros do partido, entre outras coisas. Embora a discussão da aventura nunca seja explicitamente dado, podemos deduzir da longa conversa que outros assuntos foram discutidos.

You have had some very strange adventures, I hear,’ said Glóin. ‘I wonder greatly what brings four hobbits on so long a journey. Nothing like it has happened since Bilbo came with us. But perhaps I should not inquire too closely, since Elrond and Gandalf do not seem disposed to talk of this?’

‘I think we will not speak of it, at least not yet,’ said Frodo politely. He guessed that even in Elrond’s house the matter of the Ring was not one for casual talk; and in any case he wished to forget his troubles for a time. ‘But I am equally curious,’ he added, ‘to learn what brings so important a dwarf so far from the Lonely Mountain.’

Glóin looked at him. ‘If you have not heard, I think we will not speak yet of that either. Master Elrond will summon us all ere long, I believe, and then we shall all hear many things. But there is much else that may be told.’

Throughout the rest of the meal they talked together, but Frodo listened more than he spoke; for the news of the Shire, apart from the Ring, seemed small and far-away and unimportant, while Glóin had much to tell of events in the northern regions of Wilderland. Frodo learned that Grimbeorn the Old, son of Beorn, was now the lord of many sturdy men, and to their land between the Mountains and Mirkwood neither orc nor wolf dared to go.

[...]

‘And what of your own people?’ asked Frodo.

‘There is much to tell, good and bad,’ said Glóin; ‘yet it is mostly good: we have so far been fortunate, though we do not escape the shadow of these times. If you really wish to hear of us, I will tell you tidings gladly. But stop me when you are weary! Dwarves’ tongues run on when speaking of their handiwork, they say.’

And with that Glóin embarked on a long account of the doings of the Dwarf-kingdom. He was delighted to have found so polite a listener; for Frodo showed no sign of weariness and made no attempt to change the subject, though actually he soon got rather lost among the strange names of people and places that he had never heard of before. He was interested, however, to hear that Dáin was still King under the Mountain, and was now old (having passed his two hundred and fiftieth year), venerable, and fabulously rich. Of the ten companions who had survived the Battle of Five Armies seven were still with him: Dwalin, Glóin, Dori, Nori, Bifur, Bofur, and Bombur. Bombur was now so fat that he could not move himself from his couch to his chair at table, and it took six young dwarves to lift him.
_{Book 2, Chapter I: Many Meetings}

Nos capítulos posteriores, qualquer menção a Glóin é meramente descrever Gimli como seu filho, em oposição às discussões entre Gimli e Frodo sobre Glóin e Bilbo. Entretanto, houve muito tempo em Rivendell para que essas conversas tivessem ocorrido, e é bem possível que elas tenham tido.