How to deal with the neighbours?

I am kind of having problems with my upstairs neighbour (english man ) who owns his apartment above, mine I rent from the landlord. The tone of upstairs neighbour is that of I own mine and you rent yours so what I say goes. I kind of feel that his polish girl friend is behind his attitude as he seemed so nice when she was not there. For example he wanted to use the private garden which is part of our property for his personal use, so he lied that the landlord misinformed us and it is for his use as well, which later turned out to be our private use alone and landlord doesn't want them to use it.

Another instance is that when landlord carries out somework in our property he gets annoyed and comes for an argument with us. He doesn't understand we do not even know who send the workers as we were also not informed and to always speak with the landlord.

As it got so bad, my partner left a note requesting to contact the property manager for all concerns regarding us or apartment than to speak with us, implicity informing him not to speak to us ever again. But for some reason he is too good to be true all of a sudden and it is kind of surprising me?
Is it better to stay away from him?
Any advice much appreciated.

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