Because mine doesn't work on the other one, I want to change a new one.
Change a new ID on the new mobile phone, because the ID on the old mobile phone, I can't log in on the new mobile phone.
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Why can't you log in with the old ID? What happens when you try? Error message(s)?
When changing to the new ID, make sure you turn off Find My Phone before signing out of the old ID. Once signed out and Find My Phone is off, then sign in with the new ID, then turn Find My Phone back on. 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.
How to switch Apple IDs on your iPhone or iPad.
What to do after you change your Apple ID or password - Apple Support.
How to transfer all files from one iCloud account to another.