Thank you. Looks like I have to follow the following steps:
Step 1: Insert the SIM card with the new phone number into the old phone and register the new number in the old phone.
Step 2: Insert the SIM card with the new phone number into the new phone and register the new phone number in the new phone.
Step 3: Restore the back up from iCloud.
Correct?
This would be a problem for me because I cannot insert a new SIM card with a new number into the old phone for security reasons (a corporate phone). The new phone is a private one.
Any other way?