when we got a second dog that wsnt used to cats, our cat wouldnt come home and we were really scared she would leave us, so we bought a small size kennel, put it 6ft off the ground in the garden near to the back window of the house,with a waterproof tarpaulin above and a cat ladder, made it cosy and put catnip inside.
t was her sanctuary, after about three months and she got used to seeing the 2nd dog in the garden and they made friends she came home again, we still got the "sanctuary" in the garden, didnt have the heart to remove it, she uses it to get out of the rain sometimes.Maybe your stray needs something similar or as suggested a cat flap in the shed but not big enough for a fox to get in also.
How about moving his food a liitle tiny way into the house bit at a time ? he has probably never been inside a house before.Good luck nice to know that people still care.