Why not just ask him? If you are that concerned about what he is emailing, then you shouldn't be together
How Do I Get My Boyfriend's Email Passwords?
You shouldnt have to be checking his e-mails or even trying to find ways to be sneaky about it. Be straight up and ask him and if resists then hes hiding something, don't make it look like your searching for something if you really want to catch him.
This requires a very sophisticated procedure. First thing you do is: Mercifully break up with your boyfriend, as surely, the relationship will not last. Then you sit in a dark room for hours all the while chanting for the passwords.
You just get your boy friends e-mail,get every information you need about the guy for instance his birth day date and then type the email id and then click on forgotten my password then you use the informations you have gathered to answer the questions asked