Hi there!
It sounds like you’re using third-party accounts (such as Instagram, Facebook, etc.) with Duo Mobile. In order to restore these accounts onto a new device (with the same platform as your old device, as in this case) you must set a recovery password for the account(s) in Duo Mobile on the old device.
Then when you restore Duo Mobile from a backup to your new device, it should detect that you have third-party accounts protected and prompt you to reconnect. You can then enter the recovery password when prompted to restore these.
Please check out our guide on Duo Restore for Third-Party Accounts for more information.