Hello XXXXXXXXX,
Welcome to Just Answer.
Sorry to hear about your problem.
You owe your neighbor absolutely nothing. It his his fence, he owns it and any repair/ maintenance is his responsibility. It should be installed on his side of the property line and not on yours. He is correct in that you cannot attach anything to it without his permission.
If you need further help or clarification on this answer, please do not hesitate to reply to this post.
Thanks for asking your question at Just Answer.
Best of Luck, Brian
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Architect
Licensed Architect- 12 years, L.E.E.D. AP, Former Remodeling Contractor- 10 years