Well the good news is, when your stepson is ready, rehab can work. My son was never clean and sober from 12 to about 28, except a few months he was in jail. But when he was finally ready, and I had found a good program, he did very well - it took two six-month stints - and now he's been clean and sober for more than six years.
(Last week he told me "I blew it!" - he broke his ankle and the doctor gave him an addictive drug for the pain. But he only took it for about 24 hours, til the pain was reduced, and just ibuprofen since then. So no big deal.)
While he was in rehab, I met a bunch of other "students" there, and most of the staff was recovering addicts - people with horrible pasts but clean and sober for many years. There is no doubt that a good program can work, and an addict can get into recovery and have a great life even after many years of using, lying, and stealing (which all pretty much go together).
But... .
SS22 is an addict who has been to a number of treatment programs, but has often maintained he isn't an addict, he just went through an "addictive phase."
... .which makes it clear that he isn't ready. His mom is "enabling" him - most addicts have at least one person in their lives fixing their messes and allowing them to keep using without experiencing the consequences of their behavior. But the key is for your stepson to decide he that he has a problem and needs help, and that he is ready to accept help; til that happens there is very little you can do.
You can let your stepson know that you care about him and you want what's best for him. You can offer to talk with him when he wants to talk about his issues. You can let him know that you have looked into options - I checked out every rehab facility near where we lived so I knew what options there were - and you can talk openly with him, if he wants to, about what options there might be that would be affordable, and if you would be able to help pay for it, or help him find some other source of funding. (Funding is one of the biggest reasons addicts give for not getting help.)
But beyond that, you can't fix him or "make" him go to rehab. And as long as his mom continues to enable him, you probably can't make an "intervention" work - that requires that all his options are closed off except rehab.
So... .you will probably need to hang in there and make sure he knows you want what's best for him but that you won't enable his drug use. He may have to reach his "rock bottom" - something worse happening to him - and there's no way to know how low he might have to go before he decides to get help. For some addicts it might be something not too bad, like waking up in your yard. For others, it might be worse. My son had to go to prison for four months, then get out and relapse within 48 hours - and get busted by his probation officer and taken back to jail - before he finally accepted that he needed help.
It's a very difficult thing for a parent to accept that this is mostly beyond your control, but it's a fact and you can get help too - try Al-Anon or find a counselor for yourself (I did both of those).
I wish it was easier but I've followed the progress of quite a few people I met at my son's rehab, and that's how it works - we work on our own acceptance until the addict decides to get help, and then while he gets help, and afterward, we work on our acceptance some more, because there will never be any guarantee that he won't relapse, even after rehab. It's a forever thing, but once he gets help, if he's committed, it can go much better.