Hud Housing And Annulment Nh

So I’m trying to get my boyfriend into income based HUD housing with me, but the problem is he has a bit of a record. 2016-2017 he got 3 possession/transpiration charges of a small amount of marijuana. The last charge he got a suspended sentence on a transportation of controlled substance in 2017 and it was misdemeanor a with a suspended sentence that got brought up in 2020 bc of another incident but that charge ended up being nolo prosique, he still had to do the time though. Anyways we are working with a lawyer trying to get them annulled but he said that misdemeanor a is not up for annulment because of the the suspended sentence being brought up, and he’s not sure any can be annulled bc not all of them can be. is that true? If so what would be the likely hood of him being rejected for those charges from HUD housing