This tutorial explains how to transfer contacts from iPhone to iPhone using an iTunes backup.
- Open iTunes on your computer
- Connect your old iPhone to your computer via USB
- Your iPhone should appear in the top row of buttons in the iTunes window
- Select your iPhone in iTunes
- This will open the Summary page
- Select This computer and click Back Up Now (This will create a backup of your old iPhone, that will be saved on your computer)
- Start the setup process on your new iPhone (Make sure to log in with the same Apple ID you used on your old iPhone)
- Restore your backup by selecting Backup from iTunes
- Once the backup restore is completed, the contacts from your old iPhone should now be available on your new iPhone