HE can't "donate" it to anyone; he can abandon it to BATFE or the police. In theory, he could abandon it to a museum owned by a political entity, but that path is iffy and could lead to more trouble.
I recommend calling BATFE because they deal with that kind of thing all the time and are actually less likely to want to throw someone in jail than a politicized police or sheriff's department. Stripping the gun would make sense, but is not in the spirit of "immediate notification" BATFE requires once the person becomes aware of the law violation. ("I'll surrender the receiver next week after I take off all the parts" won't go over too well with the Feds.)
Here is the CFR basis for a Form 10 registration:
Registration of firearms by certain governmental entities.
Any State, any political subdivision thereof, or any official police organization of such a government entity engaged in criminal investigations, which acquires for official use a firearm not registered to it, such as by abandonment or by forfeiture, will register such firearm with the Director by filing Form 10 (Firearms), Registration of Firearms Acquired by Certain Governmental Entities, and such registration shall become a part of the National Firearms Registration and Transfer Record. The application shall identify the applicant, describe each firearm covered by the application, show the location where each firearm usually will be kept, and, if the firearm is unserviceable, the application shall show how the firearm was made unserviceable. This section shall not apply to a firearm merely being held for use as evidence in a criminal proceeding. The Form 10 (Firearms) shall be executed in duplicate in accordance with the instructions thereon. Upon registering the firearm, the Director shall return the original Form 10 (Firearms) to the registrant with notification thereon that registration of the firearm has been made. The registration of any firearm under this section is for official use only and a subsequent transfer will be approved only to other governmental entities for official use.
Jim