A free program for Android, by Jan Berkel.

SMS Backup + is an app that makes it easy to back up all of your SMS messages, MMS messages, and call history to a safe place, so you can restore it if you ever switch to a new device.

This is a free open-source project that has been in active development for a long time, completely ad and tracking-free.

It is very easy to use the app and back up your SMS, MMS, and call history. Just make sure that it is enabled in your Gmail account. It can also be backed up in Google Calendar.

Having this app, you will no longer worry about your important messages or call history being deleted because you are now backed up.