What is the correct course of action and expiation for adultery after a husband repents of it?

The Muslim who has committed adultery must repent and conceal himself, and no expiation is required of him. If his adultery is proven to his wife, she must conceal it and live with him as if nothing had happened, and she should help him maintain chastity and warn him against the causes of immorality. It is not permissible to investigate the adultery of either spouse, for the fundamental principle regarding a Muslim is their integrity.