The back of my head is flat and balding, can a hair transplant fix both?

I had a very famous celebrity who had a hair transplant with me which he loved. When he came back to see me, he asked if I would transplant his crown because he hated his flat crown. He envied people with a nice rounded head.  So at his suggestion, I transplanted his thinning crown and after about a year when the hair grew out to a good length, he visited me to show me what happened to his flat head.  It was GONE, or at least no one could see it under the bushy hair that was placed to life the hair high above his flat crown. His hair eventually turned white and when he performed on the Vegas Strip, people from the audience would always ask him: “Is that hair all yours?”. “Of course its my hair”, he responded and it was his transplanted hair that was his and my secret.