+1(514) 937-9445 or Toll-free (Canada & US) +1 (888) 947-9445
I think your question should to be
" Can one become Federal Resident after bieng accepted Quebec resident"

Well, as a permanent resident of Canada, you can live, visit or work any place of canada. Quebec too.
 
The Canada's charter of rights and freedoms, it states that a PR is free to live and work in any province of Canada so that includes Quebec.