I called CIC to ask how long it takes for the COPR letter to arrive after status changed to DM (the ecas status changed on May 2nd). The call center agent was surprised that our file was sent to Paris while my common law partner was here with me in Canada. She asked me if I notified CIC that he is living here with me, so I told her that according to the forms we sent, and according to e-cas, his home address is here in Canada.
Anyhow, she said that it may take up to 6 weeks or more for the COPR letter to arrive (since my common law partner is visa exempt), because Paris sends the letter in batches. I hope she is wrong, but I guess there is nothing else we can do. I did asked if the PR application was approved, and she said yes. We got the decision made, but you never know...