Sheikh `Abd al-Rahmân al-Jar`î, professor at King Khâlid University in Abhâ
It is permissible to have this operation done to correct your jawline, since you are returning your jaw back to its normal place. It is lawful for a person to make amendments to his appearance when some natural defect exists.
I also think that it alright for your friend to have the moles removed from his face, particularly if he suffers from their sight, whether mentally or physically. Such a mole becomes, in such a case, a defect that may be removed, as it is existence on the face is not something normal.
And Allah knows best.
Source: Islam Today