What is the way to atone for the sin of adultery, while preserving the existing marriage and avoiding marital problems that may result from the wife's knowledge of what happened?

The man must repent with sincere repentance and frequently seek forgiveness and perform righteous deeds. The conditions for repentance are: regret, determination not to return [to the sin], and complete cessation of the sin and everything connected to it. He must separate from the girl he is currently with because his marriage to her is invalid, as the majority of scholars stipulated for the validity of a fornicator marrying the one with whom he fornicated that she not be pregnant. This man married her while she was pregnant from fornication. Therefore, the fetus with which the girl became pregnant has no legally recognized relation to this man, and similarly, the first child is a child of fornication. The girl he is currently with is not his wife, and their life together is an illicit relationship. He must separate from her. If she gives birth to her burden, repents, and reforms her condition, then it is permissible for him to marry her.