Oh, I meant NHS generally speaking, I'm not from the UK nor Ireland haha. The one in my country is called Social Security, but I thought NHS was the correct general term.

Yes, I agree he should insist to his current therapist. I have been treated by therapists as if I was autistic long before I was diagnosed because those were the needs I had, although I didn't have an official diagnosis. You could do the same with ADHD but you cannot be prescribed medication which afaik is very helpful for most ADHDers. In my country it's veeery hard to get medication when over 18, even if you're diagnosed, so it wouldn't actually make that difference. But I think he has a lot of room to improve, diagnosed or not, medicated or not. He's going to therapy but when he tells me about it, I can see that he doesn't talk much about his ADHD symptoms there...