Is the forgiveness of the wife a condition for the completion of the repentance of the girl who was alone with a married man without committing adultery, then repented? And is it permissible for the girl to marry this man after he divorces his first wife?

Acquaintance between men and women is a path to fitna (temptation leading to sin). One must repent, sever the relationship, and eliminate everything that could lead back to the sin. If repentance has occurred and they are suitable for marriage, what transpired between them does not constitute a religious impediment to marriage, for the Prophet, peace and blessings be upon him, said: "There is nothing like marriage for two who love one another." Whoever repents from a sin, Allah accepts his repentance. It is not a condition to inform the previous wife.