Customized dropdown lists are specific to the device they have been customized on, but you can move them to another device by creating a backup on the device that has the dropdowns and then restoring it on the other device. We recommend you get the template/dropdowns set up how you want on a single device and then create/restore the backup on a new device. When you do this, it will replace all the data on the device you restore the backup with the data in the backup. This means that if you have any inspections on the device whose data you are replacing, you will want to make sure they have been uploaded to the portal before you restore the backup.
You can find instructions on how to create and restore backups here: How To Create and Restore a Backup