How to back up short messages in windows 10 mobil?

First, your mobile phone must be logged in with a Microsoft account. Please check whether you are logged in with a Microsoft account in Phone Settings → Accounts. If not, please register a Microsoft account and use it to log in.

After you confirm logging in with a Microsoft account, go to Phone Settings → System → Information, and make sure that "Synchronize information between devices" is turned on.

After changing to a new Windows phone, just log in to the same Microsoft account, and your text messages will be synchronized back.

Note: Windows SMS can only be backed up at present, but not exported.