An NFA firearm that has ever been manufactured, transferred, or possessed, in violation of the NFA, immediately and irrevocably becomes contraband and may never lawfully be possessed other than by the government.
Many moons ago a friend was willed a live, functional machinegun that his father captured from an enemy combatant who no longer needed it. It probably could have been amnesty registered during the one and only amnesty that has ever been held, but it wasn't. Fortunately he knew someone who knew someone that was in charge of a military firearms museum (an actual museum owned and run by the military) and he was able to donate the gun to them. They were quite happy to add it to the museum, and of course the military can possess whatever the hell they want.
Assuming that it's not possible that your friend's gun was owned by the agency and is actually registered, all that can be done is destroy or surrender to ATF. But what does "destroy" mean?
I would think that for NFA purposes it is "destroyed" if the barrel is removed and destroyed or sold/disposed to a 3rd party who does not possess a firearm with which it could be used (lest you create a new contraband gun via constructive possession). If the shotgun doesn't have a barrel it is no longer a short barreled shotgun. Then if they could acquire a legal-length barrel for it (via GunParts.com or some place that sells parts for old guns) they could make it a legal Title 1 (non-NFA) firearm again.
Note that I do not believe it would be sufficient to simply weld long tubes onto the existing short barrels. ATF has some funny rules about contraband guns being able to be made un-contraband using all the original parts. If you just weld extensions on the barrel you still possess the complete original contraband firearm, even though you have otherwise made it "legal".
For example it is my recollection that if someone wants to register a Marbles Game Getter as an AOW, and it has never been registered before, which means it was contraband at some point, the serial number of the barrel on the gun can't match the receiver - otherwise you are registering something that is contraband. But if the gun has no barrel, and then is Form 1 registered, and then assembled with a barrel with a non-matching serial number, then that's OK.
Given that, if the desire is to make a legal short barreled shotgun out if it, there might be a path to do so. If you could destroy the gun by destroying the original barrel, then Form 1 register the gun as an SBS, then acquire a replacement barrel and cut it down (or acquire a replacement barrel that is already cut down), that would let you make a legal SBS out of it.
Regarding acquiring a replacement barrel that is already cut down - there is nothing illegal about selling a short barrel to someone. The Benelli 14" barrels are for sale on GunBroker all the time. Of course if one owns a Benelli that the barrel will fit, and said Benelli is not SBS registered, and one acquires the barrel before so-registering, then one constructively possesses an unregistered NFA firearm. But if one does a Form 1 SBS registration and receives the approved form back, then one may acquire said barrel without violating the NFA.
So, if someone else had previously destroyed a contraband shotgun of the same model by selling the barrel to Gun Parts Corp., it's possible they might have one for sale that is already cut down - which of course shouldn't be acquired until after the shotgun has been destroyed by disposing of the original barrel, AND registered as an SBS, after which a different short barrel could be acquired, or a long barrel acquired and cut down.
I would strongly advise against trying to be cute and saying that the original barrel was disposed of, the gun was registered, and then a new barrel put on, when in fact the barrel on there is the original one. Even if there were no serial number on the barrel I would think it would probably be pretty easy to prove it was the original barrel and violating the NFA is a felony.
OK, that got a little long. And it was kind of stream of consciousness so hopefully it isn't too haphazard. None of this is legal advice, etc., but I have a better familiarity with NFA law and practice than most attorneys unless they specialize in it.