IOS – iPhone 5c is not found by iTunes

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So, I've got a new iPhone SE and an old 5c and I wanna transfer/sync the old one into the new one. The "bring the new phone close to an old one" and sync by bluetooth doesn't cut it cuz it requires iOS version 11+, and the 5c is on version 10.3 (and can't update to 11).

So I wanted to make a backup of the 5c through iTunes and then load the new phone from the backup. But when I plug in the 5c, iTunes prompts me with "do you wanna set this phone as new?" message:
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(the backups are from my personal iPhone, which is irrelevant to this issue).

So, then I click "cancel" and I am into the regular iTunes interface, but the phone button is not there:
enter image description here

I tried to go to System Information -> USB and the phone was there, recognized. So, my question is – do you know how to get the phone connected properly so I can make a backup. Or – any other way to sync the 5c into the SE?

Specs:

iTunes: v12.8.0.150

OSX: High Sierra 10.13.6

P.S. the 5c isn't mine – I've never worked with it on my Mac.

Best Answer

The "setup as new" or "restore from backup" choice in iTunes is a bit of a misnomer. Setup this phone as new sounds like it's going to do something like wipe the phone, but it really just means the phone hasn't been plugged in and used with iTunes, so add it as a new phone into iTunes.

You definitely do not want to restore from backup (overwriting what you have on the phone now), so choose setup as new.

A couple of references, since I know "setup as new" sounds scary: