Adult adoption question

Hi, I’m a single male New Jersey high school teacher. There’s a former student of mine who has no father in their life and this student has said I’ve become like a father to him. He has said multiple times that I’m the father figure in his life. I’ve known him and his mom, a single mother, for years. If I were to adopt him as an adult, he’s now 18, how would it work? From what I’ve read, it means legal ties are cut from his mother. I want this to be that I’ve symbolically become his father with his mother is still being his mother. Can an adult adoption work that way in New Jersey?