What is the legal ruling and what is incumbent upon the husband to do regarding his wife who messages his brother, telling him: "I only enjoy myself with you; whether anally or vaginally," yet denies the existence of a relationship between them, swearing by Allah that he has not had intercourse with her?

You must prevent your brother and others from entering upon your wife in your absence, and prevent any causes of temptation for her. If she remains righteous and you do not perceive any suspicion from her, then keep her and live with her honorably. However, if suspicion arises from her, then you should separate from her, due to the deficiency this entails in your religious practice and for fear of corrupting your bed. And if it becomes clear that she has committed indecency, then her divorce, which was conditional on that, has occurred. But if it is not clear and the wife denies it, then the divorce does not occur.