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Thanks for the answers. It seems that I was not the only one who wasn't sure who was responsible.
The Posts are still there except one, it is just the fence panels that have been removed because they fell down in my garden.
I will see if I can come to some arrangement with him to go half each. I wont hold my breath but hey it's worth a go.
I suppose you could argue that if they don't want my dog in their garden, then they should do something to keep her out . Having said that, I am too fond of her to let her wander in there.