How do I move all my iPod emails to my iPhone?
Sign in with the account details(email provider) and all your mails would be now on iPhone.
if its using email, then you can just sign into the email app to get all your emails.
iOS backups only contain Mail account settings, not the actual emails! If you have an Exchange or IMAP account that is fine, all Emails will be downloaded from the server.
If you happen to use a POP Email account you will have to backup them manually or move them to an IMAP account! For example you could temporarily setup an Gmail accont on your iPod, then move all the messages from the POP account to an IMAP folder at Gmail and vice-versa on the iPhone.
Generally, the e-mails are saved on the mail server, be it Gmail, Yahoo, Hotmail or iCloud. All you need to do to bring your emails on your iPod to your iPhone is sign in to the same account and it should show up on your phone looking identical to how it looks on your iPhone
icloud: .Back up your old device to iCloud by going to Settings > iCloud > Storage & Backup
iOS: Transferring information from your current iPhone, iPad, or iPod touch to a new device
Emails should be saved by your email provider (gmail, hotmail, yahoo, etc.) so all you should need to do is set up you email on your iPhone. Go to Settings>Mail, Messages, and Calendar, select your email service, and enter in the information necessary and after a couple moments you can open up the Mail app and get to your emails.