Similar to selling your car privately. There are some forms involved to recognize that you no longer own nor are responsible for the gun in question. It’s probably a little more strict and polished now (maybe not), but it wasn’t that long ago that you kept a copy in case the cops came knocking looking for the gun and a copy got filed away in a drawer somewhere for basically the same reason. I can’t remember if gun stores were in charge of the records for private sales (which wouldn’t make sense) or if they were filed with the town/state, but it was all physical paper in a drawer somewhere regardless. There wasn’t like a system actively tracking ownership - so long as both parties had a LTC, they were okay and third party sales could be done anywhere.