Restoring backup of one phone to a different apple id

My wife and I used to share one apple id across our devices (iPhones and iPads). I just picked up an iPhone 8 and am setting it up with her own unique apple id. Prior to setting up the new phone I backed up her old iPhone 6 to our shared cloud storage which is under my id. Is there a way for me to restore that backup to her new phone under her new id?