He'll need his "US-issued Alien or Admission number (AR#, USCIS#, or 194#) for Question #13 on the 4473. This should be on his "Green Card". And he'll need his government issued photo ID with residential address (i.e. driver's license.)
On the 4473, he'd select "Other Country/Countries" and specify "Canada" in the space provided. Otherwise, he answers all the other questions exactly the same.
Also, in my experience, whenever I've done a check on a non-US Citizen, it always comes back with a "Delay" response. I also exclusively use E-Check, and I think they used to dump e-check requests to the end of the "further review" queue. In theory, that no longer happens, the "further review" regardless of initiation type, get in line "first come, first served."
But I haven't had a non-US citizen buyer in quite a few years (he got his Citizenship a few years ago), so I'm not sure if the NICS response times have changed in that regard.