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Hello I am a solicitor with 20 years experience. I will try to answer this for you.
Have they got any evidence that it is the tree causing the cracks? If not then yo do not need to do anything. If it is in fact the case that your tree is causing the problems then it might be that you are responsible fro the damage but not necessarily. There are many reasons why cracks appear in buildings other than the presence of trees nearby. Has he got a surveyors report? Have you seen the cracks? Or is he just continuing his campaign against the tree?