I'm not clear on when exactly he let HR know, but the original post makes it seem like he let them know a week before. I think at least a couple months notice makes more sense depending on the duration of leave.
I agree that employees should give sufficient notice for something like that. But even if they don't, that's not grounds for firing. It might be grounds for disallowing the leave until the required notice period has passed, assuming that's documented and legally allowed.