Yes, pretty much have to sit back and wait. If your info was entered correctly, AND you have your shooting range listed with PR, thats pretty much it. The retailer (especially PR, but pretty much all online retailers) knows what needs to be input, and would have reached out if anything was missing.
As for the wait, really depends on where you live. Nova Scotia has been absolutely dragging their asses, sometimes taking as long as three (3) whole days to approve a transfer. Not sure where alberta is right now, all my stuff in bc has cleared (up to early july), and in Ontario (and, apparently Quebec)... just be thankful that PR is storing your guns for free. Until Christmas at the earliest...
I'm in Ontario, the worst for transfers from what I've heard.