Full Stop!
This question comes up all the time, the individual should contact a reputable machinegun dealer who can access the BATFE on her behalf.
The problem being that the gun may have been registered in '68 or earlier, and the paperwork gone astray.
Apparently, because tax records are confidential, and the registration is actually a tax, it may require an access to information request.
I would recommend someone like Black River Militaria Main Page bmg17a1@gmail.com
---------- Post added at 10:08 AM ---------- Previous post was at 10:05 AM ----------
2 main problems are apparently that the BATFE records are VERY incomplete, and they are deemed to be TAX records, and therefore only confidentially held.