I'd be surprised if they got planning permission to build up to and on top of the party wall/boundary line. My council would never have granted this, I know because I asked them.

Can you describe it better? is this in what was previously a garden? what sort of boundary wall did you have before? and now presumably nextdoors extension protrudes a few inches onto your side beyond the wall/fence that was there previously.

I'm sure you can come to an agreement with him to agree for you to tie in to his extension. If you can't you could go down the route of getting nasty with him, solicitors letters telling him he is trespassing on your property and asking him to remove the offending structure. (this is why planning authorities do not allow building on top of the boundary).

Wig