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There's apps that do backups. That's the closest that can be suggested. I use SMSBackup+ that connects to my GMail. There's others out there, depending on what options you want and need.
I use SMS Backup & Restore. It uses the internal storage or SD card to save to but can also save to online locations as well. Rooted devices have a lot more options for saving and restoring text messages.
Google backs mine up to Drive.
Restores them when phone restores .
Have you taken a look at the suggestions above? Please let us know if that helps.