Some one is feeding my cat!

[ProperVexed]

DCat is a frightful glutton. He has put on weight steadily since I adopted him. I am not over feeding him, and my vet is in agreement with me.
DCat is very sociable and spends a lot of time in the gardens of a neighbouring block of flats. My DS has recently moved into the flats. He has seen DCat waiting outside a communal door and being let into the stairwell which serves 6 flats. We are pretty sure he is being fed in one of the flats and think we know which one.
DCat is getting dry overweight and I am worried about his health. He wears a "Please do not feed me" collar.
I'm debating writing a letter pointing out the problem and requesting that the occupant stops feeding my cat.
Any tips or ideas?

They may not be actively feeding him - he may be sneaking through a cat flap or open window and stealing food, he may be eating local wildlife or he may be eating bird food.

We adopted an abandoned cat who did all of the above.

We were also "cat burgled" by the cat up the road who found a a window left slightly open by dd when we were on holiday. We thought that we had had burglars but the only thing missing was 7kg of prescription cat food where the bag had been chewed open