The civil marriage is not marriage. Marrying a non Muslim man is not marriage. This is fornication and Zina.
Converting the boy and remarrying the couple is not permissible in this case as she is a fornicator and can’t marry until she repent. He is also an adulterer and can’t marry until he truly accepts Islam and repents.
If he pretended to have accepted Islam just to marry her, this marriage is still void and they are living in sin.