I moved after approval, before stamping. I filled the new address during the stamping. Faithfully they mailed the card to the old address. However, the post office forwarded the GC to my new address. I got the GC in a plain envelop - no DHS from address - jut the CSC address in Laguna Nigel and no return service requested marked. It looked like another Credit Card mailer.
May be I was just lucky. Still waiting for the spouse's card - it was mailed yesterday.