@Louie Hegeler-Meile , Thanks for posting in Q&A. From your description, I know you have two iOS devices, and device A is a new device which enrolled by Apple Configurator, device B is an existing personal device without enroll. You try to use quick transfer to transfer data from device B to device A, when the transfer is over, the management profile on device A is gone. If there is any misunderstanding, feel free to let us know.
According to your description, I found that your situation is different from the one in the article.
https://learn.microsoft.com/en-us/mem/intune/enrollment/backup-restore-ios
In the above situation, we backup the enrolled device and restore it to a new device. In your scenario, it seems we back up an unenrolled device and restore it to an enrolled device. When the new device is restored from the backup, the previous management profile will be overwritten. I think this is by design.
For your situation, I suggest enrolling the new device after the restoring is finished to avoid the management profile removing.
Hope the above information can help you.
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