"my ex is seeing a girl shortly after our breakup and now he is emailing her" . . .okay, so he's kinda moving on
"from a certain email that he knows i have the password to." . . . so he wants you to know he's 'moving on'
That sounds kind dumb on his part, it's like him trying to show you he's ignoring you or something? . . . if anything email him and tell him to change his password since you know it and move on.
You post, you ask questions, you give facts --> I reply, I give quotations, I have opinions