Hello JerryS1,
Don't get cute with the straw-man purchase, soldier. Both Florida and Federal law requires intent to be the ultimate owner of the handgun at the time of purchase. The state of mind called intent, can be proved by documentary evidence and actions, both before and after the fact. You would be taking a big chance now to try and do something like that. And it's not actually necessary.
Both Federal and Florida law recognize the possibility of double residence. The most glaring example is an out-of-state college student. Your wife's situation discloses that she is a resident of the state of Florida. Florida recognizes many different ways of establishing residency. Voter registration, applying for homestead exemption, enrolling kids in school, etc. Being the wife of a serviceman stationed in Florida can certainly attain that purpose.
I am assuming that therein lies the main issue with regard to the situation. I am not examining any other possible disqualification.
If you are stationed in Tampa, let me know. I can probably solve the problem. Free of charge. If stationed elsewhere, contact the nearest JAG. I'm certain they will be happy to lend a hand.
The only reason I could think that the FBI would be presently involved is that
Academy has a big situation undergoing and your wife's case is not the only one. As said before, BATFE is the one with the authority to conduct audits. Unless the matter has gone beyond that stage.