Export email accounts/settings from S4 to S4 Mini?

[SiamSam]

Hello, I'm trying to find a simple solution for transferring all my email accounts, passwords and settings from an S4 to a S4 Mini. The backup feature to the Google Cloud didn't work due to an "unknown error", so I used Smart Switch to migrate over most of the other phone data and settings. I just need a way to migrate all the email over now, so I don't have to set it all up again manually.