Unfortunately he doesn't have much choice
He might just about get away with the first cheque as possible back pay/arrears but not the second payment.
The amount will have to be paid back eventually , so the sooner he lets them know the better. If he tells them he's already spent it, so can't afford to pay it back immediately, they may give him time to pay it back.
BUT, if he claims to have spent it, then the DSS may find out and not pay his rent.
So despite the temptation, his best bet is to put the money into a separate account and let his former company know as soon as possible.
You never know - they might be so embarrassed they'll let him keep it!!
Good luck