She should confront him about it, but forgiving him is up to her.
Keep in mind, though, that although adultery is cause for separation/withholding the marriage debt indefinitely, she will never be free to remarry as long as her husband is alive. So think long and hard about it.
The wife (or husband, if roles are reversed) always has the option of "forgiving" or "not forgiving" adultery. If she opts for non-forgiveness, she can withhold the marriage debt indefinitely. I believe you'd have to physically separate in this case, as otherwise it would be a source of temptation for the husband. But once she forgives him, she can't change her mind later and "un-forgive him" for that same offense.
This is Catholic doctrine, by the way.
"Till death do us part."
A bad marriage or failed marriage is not a non-marriage.