Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. What this woman is doing is a great evil and an obnoxious act, which she should not have done in the first place and must stop immediately. It is forbidden for the woman to stay in seclusion with any alien man let alone having some forbidden relations with him. Now, you should exhort her to do the good and avoid the bad. Advise her, for the sake of Allah, making clear to her that what she is committing is Haram. Warn her against the Anger of Allah and His punishment in this life and the Hereafter. If she stops, that is good, and you should conceal that from all people and it is unlawful to talk about her to your husband, or your friend as this is more harmful than harmless. It is making bad deeds public and it is a form of backbiting which is forbidden in Shari'a. But, if she does not stop this sin after the exhortation and orientation, then you can warn her from the scandal and tell her that you would tell her husband if she does not leave this bad act. However, you should not, under any circumstances, tell her husband of the name of the man with whom she had the affair as this might lead to greater depravity and evil. On the other hand, you can inform her husband through a anonymous call or letter telling him to keep an eye on his family while abroad. Perhaps, such a hint would let him do what he should do. As for you, stay away from slander as it is very bad and forbidden. Allah knows best.