You mean like cheating on your spouse and letting your kid get abused?
Also if the computer is jointly owned , its not criminal by law standards.
If the emails were already on the computer, like in outlook, then yes. If he accessed her email account on the provider's server, then no, that's unauthorized access.
I'm not sure the prosecutor has any jurisdiction though; wouldn't the "crime" have taken place where the servers were located? Unless it was a local service.