My next door but one neighbour is about to finally move out, after about 5 months virtually living with boyfriend, but coming to and fro the apartment (I am in a house next door to the little block).
She has/had two cats. A black one, probably less than a year old, that has been left in the apartment mostly all of the time; and an older one who has always roamed the complex and back road and who has been in my house a lot, comes onto the garden (catches rodents but not birds strangely) and has virtually adopted my friend who also lives in the apartments. It seemed that he was effectively left behind and we have cared for him with all kinds of food (he became very underweight and scruffy at first but now his coat is like silk [maybe we should all eat cat food!], he has a mix of some dried and some wet, and has really improved since we added the pouch food.
He is nicely looked after by us jointly - and now allowed to stay in overnight (previously, not - and mainly his choice - he is very nocturnal). He waits for my friend to come home, and he also seems to know when I will go round but sometimes totally indfferent and stays in one of his many beds/spots. For example, last night, I had my Saturday pizza with the plate resting (lightly) on his head. He will not get off my lap until I tip him off....
Please suggest any way I persuade her to leave him with us. She and I are not especially friendly (due to anothe nasty neighbour - now gone- influence) but I have never said a nasty thing to or about her or her little boy, and she knows what the cat has been doing. But now, her actual move out is imminent, and I have heard (from another neighbour) that she plans to take him...... He was not happy in her home before, as he seems to like quiet, and she has a big boisterous dog and a (I think) 6 year old - and of course the other cat..... I would not criticise any of this - but I really want to plead with her to leave him with us, where he is doing so well, and is such a help to my need to look after something.

He keeps his opinion to himself when I play the piano..... but that eye speaks volumes 