GoKawiilGoogle explains how to move Authenticator codes to a new phone
Google Authenticator versions 6.0+ on Android and 4.0+ on iOS automatically sync two-factor codes to the cloud when linked to a Google account, letting users recover them by signing into the same account on a new device. Users who prefer not to sync via Google can instead manually transfer codes by exporting a QR code from the old phone's Transfer Accounts menu and importing it on the new one.