We used to have a cat who would visit a house about quarter of a mile from us. Originally, he went "missing" and we put posters up. The couple from this house telephoned to say Alfie was with them and they presumed he was a stray. We took him home and days later he was back at the couples. So we gave them our phone number and said to ring if he returned. He would visit all the time and in the end, Alfie went missing for good. At the same time this couple moved house. We believe they took him with them. We were sad to have lost him, but he was obviously happier with this couple.
I took a parcel down to my neighbours about 1/4 mile away, followed by the cat. He opened the door, cat walked in and he said "oh hello, there you are" to the cat. All the time I'd thought she was out and about she was doing the same as your cat - lying in their lovely warm conservatory being stroked and groomed. She was never fed and always reappeared around 6pm at ours looking very pleased with herself. Sadly she's no longer with us as she had to be pts in January with a huge tumour on her lung - I miss her so much as she was such a character.