The only real answer is to contact a lawyer and see what is possible and how it might be done.
Personally, I don't think it's a good idea for a felon to go to the police for advice on anything to do with guns. That could raise all kinds of red flags and that's the last thing he needs. I'd say pay for advice from a lawyer so the matter can remain private, even if the answer is that it's a no-go.
On the face of it, I'd say he's going to have a very uphill battle at this point. IMO, being sober for just over a year isn't going to impress many in law enforcement or the judiciary after 3 DWIs. One is bad, two is really, really bad, but three . . .
And that's assuming he supply convincing evidence that he is, in fact, sober and has remained so. If he hasn't been documenting every treatment session, AA meeting, or whatever, he should start as certainly that will come into question at some point.
Grouse