This is nonsense
He's not harassing the OP. How dramatic of you. Why does he have to give notice to her when she's been happy to check in on the cat? Most people would think like that.
If you were neglecting a cat you wouldn't ask a neighbour to check in on it. How do you explain that?
Also do you have proof that they didn't find someone in 24 hours? Just another assumption.
This is normal for a roaming cat to be left to it's own devices and checked in on when people go away. It's also normal for people to overfeed their cats and not give them the best diet in the world, and for cats to poo and fight with other cats.
The cat is sheltered, fed, watered, neutered, vet registered, checked up on, and taken care of. These are facts, everything else is speculation.
The reason she's posting is because she doesn't want the cat around her garden and her cats because of it's behaviour which is fine and also understandable. She can tell the neighbours that she needs to shoo the cat away because it fights with hers so she can't come round and check on food when they're away. She will keep an eye out if it's in trouble though.
This is how neighbours are supposed to interact with each other. They don't go claiming neglect, calling authorities, and stealing neighbours cats and driving out to the middle of nowhere to dump it at the drop of a hat.
People like you are so irresponsible, egging people like the OP on to cause trouble for herself when you just assume the worst case without thinking it through.