iPhone Jailbreak Experts - Accessing the email storage?
Unfortunately, emails are not backed up by iTunes/iCloud, so you'll need to go deep into the filesystem (you need to be jailbroken).

Assuming you are, then these are the steps you need to follow:

1) SSH into var/root/library/Mail
2) The mail database is contained inside a file called EnvelopeData. There is no .sqlite extension, but it is an SQLite database
3) Open the SQLite database using a program like MesaSQLite
4) Extract

I haven't personally tested this, but it should work.