At the Vets this morning, I also paid to get him tested for FIV. The Vet just called to say that test is positive, so him staying with us is not now going to be possible I don't think, as we don't want Betsy to get infected.
FWIW the risk of this is pretty low. It's usually transmitted during fights - proper fights, not just hissy swipy scraps. In your position I'd strongly consider keeping him.
https://aspengrovevet.com/feline-immunodeficiency-virus-infection-fiv/ (have a look at the "How do cats get FIV?" and "One cat in my household is FIV-positive and the others are not. What should I do?" sections)
Well done for taking care of him :-) Even if you do end up deciding it's too risky then he's had a much better chance at life because of your efforts than he'd have had without.