Owner of plant that has climbed over wall

Dear PAO,

My friends and I started collecting plants early last year, and I have really enjoyed taking care of them. I planted one of those that I purchased in a small patch in our grounds, which turned out to be a vine that has climbed on our wall. My parents have no problem with it because they appreciate the beauty of the plant. However, we are not sure if our next-door neighbor feels the same way. Although he does not appear to be mad, he said that if there will be more branches of the plant that will climb over his side, then, that would be his already. Is this true? Will he be the lawful owner?