Many of us have had dealings with the RSPCA and know that they pts FIV positive cats. Also, they'll only keep an animal for a limited time before pts, unlike some rescues who keep them untill they find a home and only pts if ill. Check the local CP's policy too. The Birmingham CP pts FIV positive cats, but this is not the policy in all areas. If it was me, I'd borrow or beg a feral cat trap - even though he isn't feral, you can't handle him - from a local vet or rescue (try googling for smaller cat rescues in your area). Trap him, take him to vet to scan for a chip; if he's not chipped, put a collar on him with a note asking if he belongs to anyone and giving your phone number.
Also ask the vet to check if he's neutered, and that he is a he!
Take him home and while he's still in the trap, allow your cat into the same room, but not too close and see how your cat reacts.
If you have no response from the collar trick, consider homing him yourself by putting his pic and details on CatChat. This way you'll know that he stays alive. On the other hand, he may be so devoted to the area that you could consider whether he can live a happy life as a "garden" cat. Is there shelter for him when it rains? Could you or your boyfriend built him a warm hutch which he can go into out of the rain and cold?
Start by trapping him and taking him to the vet for a check-up. If he/she needs neutering, you may be able to get vouchers covering the full cost; just claim that he's feral: in effect he is. The vouchers are paid to the vet, so you'd need to get this sorted beforehand.
You may want to deflea and deworm if you're prepared for the expense; you can always claim this from the owner if he has one.
Good luck. Please don't rush to the phone and ring the RSPCA