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How to transfer contacts from iPhone to iPhone without Apple ID?
Use iTunes to create a full backup of your old iPhone on a computer, then restoring that backup onto the new iPhone. This is free but time consuming approach for transferring contacts from iPhone to new iPhone without iCloud after setup.
Connect the old iPhone, trust the computer when prompted, then click "Back Up Now" to save everything, including contacts, to your computer.
Once the backup is done, disconnect the old iPhone and connect the new one. In iTunes, select "Restore Backup" and choose the backup you just made.
Keep in mind this restores everything from the old phone — apps, settings, messages, and contacts so it's best suited for people setting up a brand new iPhone rather than just moving contacts selectively.
The new iPhone should also be on the same or newer iOS version as the old one for the restore to work smoothly.