"Does he have a work permit?"
Translation:Anh ấy có giấy phép làm việc không?
I feel your pain =( To me, it does make sense to use "làm việc". I think it's best to try to think of the "work" in "work permit" as an adjective. So we can think of "giấy phép làm việc" as a "'working' permit". I know it's a bit of a stretch but that's all I got. I hope that kinda helps??