Reply I got from an email
We are not sure why it is not showing in eForms and we cannot restore it at the present time. The form will remain in the NFA system for any future need. Our apologies.
Ha, wow. What a response. I'm sure if you ever encounter an ATF agent or some overzealous cop, they'll accept that as proof of taxes paid.
He should still have the original email they sent him with PDF files attached of the approved form. Print several copies from there instead of the ATF website.