Please use Menu -> Backup & Restore on the old phone, making backup, and then restore on the new one.
It's a single encrypted file containing all your account and folder settings, and app settings.
You can transfer the file using a file manager (it's in a folder called "backup/AquaMail" off of the device's large built-in storage) -- or you can let the app upload to / download from a cloud sync service (Drive, Box, OneDrive, Dropbox). You'll see a checkbox for that when making backup, after you press Backup, when the app prompts you for the password.