I use Super Backup Pro which does a very nice job for messages, contacts, etc. and backs them up to both your phone storage and to the cloud like Google Drive if you choose. I have had occasion to recover my txt messages and found it east to use recovery and I got all the messages contained in the backup restored quickly and completely.
I have att well my note went wacky and they sent me a replacement. I ended up with all my text messages from last August 21 when I got the note after I rebooted it