How can my friend prove his email was hacked and used to send emails not from him?

My good friend has an Tmobile G1 (Google Phone) and his Gmail was somehow hacked by his verifiable insane ex who proceeded to send emails of inappropriate pictures of him out to jobs he has applied to, personal contacts, and his current job. She also sent a lot of fake stuff, like requesting to be fired from his current job. He is new at his current job and they do not know what he has been going through though she calls and harasses his job. Now the job wants him to “prove” the emails were not from him. What can he do to “prove” it?