Enrol a device after restoring a backup

i would suggest to reach out to JAMF , they would be able to help you on this Migration. 

Users are responsible for taking backups and recovering from them. Backups can be finicky, and there’s nothing you can do to help or hinder this process. If users have an iCloud backup or a iOS backup on a computer from a supervised device, they can recover that backup to another supervised iOS device (or the same device if wiped and reloaded). However, you can’t recover a personal backup (managed or unmanaged) to a supervised iOS device.

Aside of providing steps to users on how to backup their devices on a PC or a Mac, and providing instructions on how to recover from that backup during enrollment there is nothing you can do.

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@DonCascone wrote:

I'm in the process of migrating our Iphone fleet from a different MDM to Jamf and for this reason we need to wipe our devices completely to enrol them on Jamf.
I'd really like to not lose everything our colleagues have on their Iphone but in my tests I can see that the backup step is just before the enrolment step.
If I proceed with the backup the last MDM is migrated to the device too but if I enrol the device on Jamf i lose the opportunity to have a backup at all.
Is there any smart way to do this that's not just saving everything on a cloud?

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Unfortunately, there's no direct way to back up devices before Jamf enrollment without potentially migrating the old MDM. Encourage iCloud backup, explore third-party backup solutions, use data migration tools if available, and communicate clearly with users about the process and potential data loss.