I bought a new smartphone and, because the old and the new one were both Samsung, I used the Samsung Smart Switch app to easily move everything (e.g.  settings, photos and more) to my new phone using the USB connection to speed up this process.
Everything worked fine but then I had problems in connecting my new phone to my PC using the Microsoft Your Phone Companion app. On the PC side, my old smartphone remain configured and I did not find a way to add a new phone and/or, at the very least, substitute the old one with the new.

I found the solution looking to the post How to fix common problems with Your Phone app on Windows 10 related to many possible troubles in using that app. The matter in my case was that some configuration related to the old phone was copied in the new one so, on both PC and smartphone sides, the Your Phone Companion app needed a reset.

On smartphone side, I went in Settings -> Apps and I searched for Your Phone Companion app. I forced stop and I clear both data and cache. Then I restart the smartphone, just in case 😉

On PC side, I went to the Settings -> Phone section, I delete the old phone and then I add the new one, giving all the right the app need to handle it:

I was requested to insert my phone number (in my case it was the same I already set for the old phone so it was already suggested): confirming it I received on my phone an SMS with the link to click in order to connect it to that PC.

After some authorizations, the synchronization was done.

Note: the PC and the smartphone must be connected to the same WiFi or you need to go in the smartphone Settings -> Advanced features -> Windows connection and set the Use data network option (IT: Impostazioni -> Funzioni avanzate -> Collegamento a Windows – Utilizza la rete dati).

Then you can see on your PC the last 25 photos, SMS, notifications, screen mirroring … all in real time: possibly you can save them  (unfortunately one by one) on the PC. I hope that in the near future versions of the Your Phone Companion app a more appropriate management of phone data will be introduced (e.g. delete feature, save all new pictures).