First of all, I would get a dehumidifier as others have stated.

Then I would get the property deed plans to see if the neighbor built onto your land. You stated he built a wall touching your wall.**********

This is wrong for so many reasons.

Once you have the property plan showing the property line , then you can take action.

Being nice of course. Nobody likes to take down a wall, or any other construction they think is ok.

Check with your city/town you live in as well. Where I live, there has to be at least 6 feet away from property unless approved by neighbor.

This could be quite a process.....but in the meantime....get a BIG dehumidifier !!!

Good Luck