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Only if you back the messages up using an app.

If you’re on an Android platform, messages.google.c@m works fine (yes, I obscured it to prevent tagging here), and has worked for MANY years now, on pretty much any platform that’s reasonably secure, you can pair it to the Google Messages app.

If you’re on iOS I’m pretty sure there are iOS compatible ways to do this, but I’m not sure they extend beyond that platform.

You can do this with Google Messages app- 

https://play.google.com/store/apps/details?id=com.google.android.apps.messaging