Yes, he can and should ask. Work assignments in prison are not automatically carried over when an inmate moves to a different housing unit, even within the same facility. The assignment is often tied to the unit or to a specific supervisor's roster, and a dorm transfer can break that connection regardless of conduct or performance.
The first step is for him to speak with his new unit's case manager or counselor and express his interest in getting a work assignment. Having a prior kitchen job on his record and a clean conduct history are both factors that work in his favor. He should be direct about wanting to work and ask what positions are available or how to get on the list for openings.
It is also worth finding out why the move happened in the first place. A housing unit transfer can be routine, driven by bed space, classification adjustments, or administrative decisions that have nothing to do with conduct. But if there was an incident that prompted the move, that could be affecting his work eligibility independently of the unit change. His case manager can clarify that.
Work assignments matter for more than just keeping busy. They generate a small income, build a positive conduct record, and give structure to the day. The sooner he gets back into a job role, the better the rest of his sentence goes.