RE: what would you have done
On the one hand it may seem like the noble thing to do by letting him have the deer, but then there is the law of unforseen consequences. What did he really learn from this? Will he hesitate to do this again in the future and does he understand that he should not shoot at game that was alreadywounded by another hunter? Does he understand that just because he fired the last bullet doesn't mean that he has claim to the kill, miss or not? Did he really become a better hunter/person by being allowed to claim a deer that was not his? I think that this was a squandered opportunity for a lesson in integrity and character, and the lesson he learned through your generosity might have been the wrong one.
Mike