Restore data from a different user ID to another Iphone-ID

I just acquired a new iphone 13-pro to my soon, but it happens he is using in his existing (old) iphone the apple ID from his sister. My soon, never had an apple ID (he was young ...).

I did create an apple-id for my soon and would like to restore his old-device existing information to his new iphone under his new apple ID (then he stops using his sister´s id)

. How can I back up his existing data (it seems pretty basic ... i just plug his cel on his Mac and back it up) creating a back up ?

. How can i restore this back up to his new iphone which is now under a different new apple ID, the one I created for him ?

Im not sure what i did wrong, i did backed up his existing data at his computer and tried to recover it to his new iphone which now has a different ID (the new ID), then it pops a "it is now restoring iphone data to new iphone ....",

But this message seems sort of frozen, i did it more than 3 times and waited more than 3 or 4 hours but it again shows this same restoring frozen message ? it seems the process does not complete or start ...

Thank you so much for any guidence on this !