If you're talking about set up of the email accounts themselves, that should still be an automatic thing as long you have iCloud Drive enabled on both devices and the Mail option enabled for iCloud Drive on both devices.
Alternatively, if you backup your device via iCloud or iTunes, that backup will retain a listing of the accounts you had set up on the device and those will be a restored when you restore a backup of your device to that device or another device again.
You may have to re-enter the passwords for the accounts after restoring from a backup, but even that can be avoided by enabling the iCloud Keychain feature will save email passwords to your iCloud account as well for retrieval.