What is the way to atone for the sin of exposing someone by taking revenge on them by publishing pictures of their wife, and is it obligatory to inform him and ask for his forgiveness, with the consequences that entails, or is there another solution?

Committing the grave sin of stealing an email and spying on its contents, especially a wife's photos and publishing them, is a major crime that carries a tremendous burden of sin. The door to repentance is open, accompanied by remorse and a firm resolve not to return to such acts. Sincere repentance erases sins. Do not tell your friend what you did; rather, supplicate for him and treat him well. Also, do not put private photos on electronic devices.