There is no Federal law regulating private in-state face-to-face sales.
There are some state laws, e.g. in California, that require an FFL transfer for face-to-face private sales. That wouldn't apply to someone in New York. Also, California's law has only been in effect since 1991, as TAB writes above.
In California, long guns are not registered or tracked in a database like handguns are.
So, even in California: let's say a shotgun was manufactured and first sold before 1991 in California. There were no other transfers, so there's no other paper on it anywhere. Your friend sold the shotgun in 1998, without any paper trail. Given that we are presumed innocent in court, how could a prosecutor prove that he sold it in 1998, not 1988?
Even in California, he would have done nothing
morally wrong, and nothing that can be proven in court, either. Let sleeping dogs lie. The fact that nobody has come knocking on his door would indicate that the gun hasn't been used in a crime (obviously, very few of the guns in America ever are). He didn't supply criminals with shotguns or anything, so has nothing to feel guilty about (unless he's a PeTA nut and regrets selling shotguns to bird hunters
).
It seems that, since he was in New York, he didn't break any laws, either. Just forget about it.
Definitely DO NOT report them stolen! This could get innocent people in trouble, and could land him in jail. It
should land him in jail if he does it: he'd be making a false report that could result in innocent people being prosecuted for a serious felony!