Is it permissible for a Muslim man married to a non-Muslim woman to remain married to her?

A Muslim man is not permitted to marry a disbelieving woman unless she is from the People of the Book (Jewish or Christian), based on the Almighty's saying: (And do not marry polytheistic women until they believe), and His saying: (And [lawful in marriage are] the chaste women from among the believers and the chaste women from among those who were given the Scripture). The woman from the People of the Book must adhere to her religion; if she is an atheist, then it is not permissible to marry her. If this woman embraces Islam, then it is permissible to عقد عليها with a new contract.