no, don't remove the stock... I know you can't have a rifle w/out a stock. one of those silly no-nos no one can really explain.
as to replacing it, someone else will have to chime in but I'd leave it alone at least until you have the other one in hand.
Yes he CAN remove the stock and it IS explainable.
So long as the barrel stays over 16 inches (18 on a shotgun) and the overall length over 26 inches...
He's fine.