Unless he has been incarcerated for the ENTIRe 6 six years of his sons life, then saying gee I was locked up for the last year or so isn't going to get him very far. Your son has a stable homelife with you and his mother.
You have a good case for stepparent adoption, especially with the bf going back and forth between prision and halfway houses. He has shown through past actions that he annot keep a stable life.
While we have been through a stepparent adoption, we have not had to deal with most of the factors that you are dealing with. In our case it was the birthmother whom walked away, and never looked back. I wish you the best of luck on your adoption journey, and please do keep us updated!
Stepparent Adoption Blog