Ele não fez
Nos livros Jeor declara explicitamente que a espada foi deixada para seu filho Jorah quando ele pegou o preto, só que Jorah o deixou quando ele fugiu. Quando Jora saiu, a irmã de Jeor devolveu-o a ele, mas Jeor o escondeu.
"It is," the Old Bear told him. "It was my father's sword, and his father's before him. The Mormonts have carried it for five centuries. I wielded it in my day and passed it on to my son when I took the black."
He is giving me his son's sword. Jon could scarcely believe it. The blade was exquisitely balanced. The edges glimmered faintly as they kissed the light. "Your son—"
"My son brought dishonor to House Mormont, but at least he had the grace to leave the sword behind when he fled. My sister returned it to my keeping, but the very sight of it reminded me of Jorah's shame, so I put it aside and thought no more of it until we found it in the ashes of my bedchamber. The original pommel was a bear's head, silver, yet so worn its features were all but indistinguishable. For you, I thought a white wolf more apt. One of our builders is a fair stonecarver."
A Game of Thrones, Jon VIII
A cena no show é menos detalhada, embora a mesma situação.
Jeor Mormont: It was my father's sword, his father before him. The Mormonts have carried it for five centuries. It was meant for my son Jorah. He brought dishonor to our House, but he had the grace to leave the sword before he fled from Westeros.
Game of Thrones, Season 1 Episode 9, "Baelor"
Por que ele guardou a espada quando Maege devolveu a espada a Jeor em vez de mantê-la na Ilha dos Ursos com a casa, bem, não sabemos. Pode ser porque ela não tem filhos, então acredita que deveria estar em possessão masculina.