I've heard if it's a rush job they can fax you a copy pretty quick, the next day in some cases if you fax it to them.
I just moved to NC from Florida and didn't have my new address until about 10 days before I loaded everything up and hit the road. I mailed the form as soon as I got the address and called them a couple of days before I left to see where they were on it. The examiner had just approved it but there wasn't enough time to get it back to me in the mail so they faxed me a copy and sent the original to my new address. Not only that but the original was returned to the ATF, I think is was because it was addressed to the trust and not me, and the examiner called me to check on the address and sent it again, with my name on it this time, and it finally arrived about to weeks after I did.