What is the ruling on eyebrow transplantation (whether natural or artificial) for someone who was not born with eyebrows and suffers from psychological problems because of that?

There is no harm in transplanting eyebrow hair for someone who has no hair there, because that is not an alteration of the original creation. Rather, it is a treatment to restore the sound creation, and it is not beautification, but rather the removal of a defect that disfigures the creation.