If your boyfriend's on probation, there's probably a stipulation that if he changes his address, he has to get his probation officer's approval. That's why she's probably threatening him about that. As for the paycheck thing, why doesn't he tell his employer that no one other than himself can pick up his check?
He might be kicked off the team, but that's part of the punishment that might not be avoidable. Just another consequence of what he did.
It sounds like his mom's trying to manipulate him to do what she wants. If he handles things as an adult and is responsible, hopefully he won't have problems.
But definitely, he needs to check into that whole residence thing.