This is now depreciated, use Authy instead, it automatically backs up your 2FA.
If you use Google 2FA on an iPhone, iPad, iPod, etc and want to be able to backup all you’re precious 2-Factor Authentication Codes (used for many of the common bitcoin exchanges), this is how it can easily be done.
Step 1: Update iTunes
Step 2: Open iTunes and connect your iPhone/iPad/iPod
Step 3: Backup
In iTunes, select your iPhone, and under the Summary Tab you should see “Backups”
Make sure you are backing up to “This Computer” and not iCloud. In addition the backup MUSB BE ENCRYPTED or else the google authenticator keys will not be apart of it.
Once completed, click “Back Up Now”
You now have a complete copy of all the settings and such from your phone, including the google authenticator keys.
Step 4: Restoring to a new/secondary device.
Connect the device and open up iTunes. Go to “Restore Backup…” under Manually Back Up and Restore. Note that this may not restore the Google Authenticator Application. In that case, go ahead and redownload it, you’re keys should be there the first time its run.