Have your COPR & passport.
Go to your nearest Service Canada to get your permanent SIN.
Go to your nearest Service (Province) to get your provincial health card.
Go to your bank and change your SIN number and have your status changed to PR. (optional I guess)
In my case, I had to go to the full service Ontario to get my Ontario health card status changed (work permit to PR).
Smaller service Ontario (privately held) won't be able to do it for you as they don't integrate with the government of Canada.