The parents were on Hannity and claimed that he registered it on the US side and they gave him the paperwork he needed to show them on the Mexican side.
They also claimed that Mexican officials and military personnel have written to the judges and prosecution that this weapon wasn’t on the ban list.
I don’t recall having to do anything on the US side to take a shotgun into Mexico. It was all done on the Mexico side. Even if permits were done on the US side, it still has to be done on the Mexico side BEFORE crossing the shotgun into Mexico. It is illegal to even take a shotgun shell into Mexico without a permit.