If you are the admin of domain B, yes, you can assign the resource permission to users in domain B.
If there are trust relationship, the admin in domain B can assign resource to users from domain A.
I'm not sure i understand you correctly when you said: users replicated from domain A to Domain B.
User objects can't replicate across domain/forests.
But the admin in domain B can assign resource to users from domain A if Domain A is the trusted domain.