Facial hair growth on skin graft. Any suggestions? (photos)

If your doctor is willing to move a graft from your beard area to the upper lip then you could grow hair without a hair transplant but this is not a common site of donor skin grafts. They are often times taken from the collar bone area or behind the ear. A transplant is possible after the skin graft is healed, at least 6-12 months. You drew a very thick line on your photo which obscures the detail of the injured area. I'm wondering why you couldn't just do the hair transplant without removing the underlying scar? It doesn't appear to distort your lips or mouth. You can use either beard hair from the lower neck or scalp hair for a mustache transplant.

Unfortunately hair will not grow in the skin graft unless you transplant hair into it. It would definitely have to wait until the skin graft healed. The best option in my opinion is the beard hair followed by scalp hair.