My father does not know if his ex- wife divorced him. how can he find out if she actually filed for divorce?

Does he know where she lives? If it were me, I would consult an attorney, by phone, in that area and have them investigate about this. Court records in the area will show whether she has petitioned the courts for a divorce. She would have had to submit a formal request for divorce, filed with the courts. Tricky situation as your father is at a disadvantage being out of the country. Good luck.