Is it permissible for a girl who was in an unlawful relationship and ended it six months ago to send a short message to the young man via Gmail merely to check on his well-being, with the intention of not resuming communication with him via Facebook, knowing that she prays to God to unite them in a lawful marriage?

We congratulate you on Allah's guidance to you, and we ask Allah to make your repentance sincere. It is not permissible for you to send a message to the young man with whom you had a relationship, as that may be a step of Satan's to turn you away from guidance. There is no harm in supplicating to Allah to facilitate your marriage to him if he is pleasing in his religion and character. If marriage is not facilitated, then strive to turn your heart away from him and ask Allah to replace him with someone better.