Mrs. Haffner-Luntzer has finished her habilitation by giving the habilitation lecture.
To be granted the title Priv.-Doz. by the University the person has to fulfill the criteria set by the University which usually require excellence in research, teaching, and further education. In its current usage, the title indicates that the holder has the permission to teach and examine students independently without having a chair. (Wikipedia)
Cordially congratulation to this next step in her career.