Apple ID
My child’s phone is attached to my Apple ID. How can I remove a device from my Apple ID and set up a separate Apple ID for that device? Do I have to permanently remove it from my account? What are the pros and cons of doing that?
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You need to permanently remove it from your ID. If you set up, Family Sharing, that should fix most of the problems transferring the child's phone to its own Apple ID.
If 13 years old or older.
If under 13 years old, you will need to set up Family Sharing to create an ID.
Family Sharing and Apple ID for your child.
When changing to the new ID, there may be some data loss, but you can minimize it. If syncing photos with iCloud, ensure Optimization is turned off in Settings/Your Name/iCloud/Photos and/or in Photos/Preferences/iCloud. Then make sure full resolution photos are on the device/computer. When signing out of iCloud, if asked whether you want to retain data, choose yes. Messages conversations will be lost if they are addressed to the ID. See the article below for other places that the old ID should be removed. See Winston Churchill's response in the below discussion. Also set up Family Sharing between the IDs to keep access to your apps/purchases.
Set up - your child’s iPhone, iPad, or iPod touch
How to switch Apple IDs on your iPhone or iPad.
How to transfer all files from one iCloud account to another.
What to do after you change your Apple ID or password - Apple Support.