I'm pretty sure that when trying to transfer the skill from the stone, it checks if the character who would 'receive' the skill is eligible for it, and so if they have not done the Spellweaving quest, they won't be able to take the skill from the stone. If I remember right, same thing happens with Mythic tokens - if you choose spellweaving but the character isn't eligible for it, the skill will not be applied and you have to pick something else or cancel using the token.