I initially purchased and used this from my phone. I was able to export tens of thousands of messages that I wanted to keep. It was a little bit clunky to do it from the phone. This week, I went to use it again and discovered the companion computer app. It is TERRIFIC. I carefully followed the directions to back up my iPhone. I had a little bit of a hard time figuring out how to choose the Backup on the menu in the app (if you make no choice, you will get a big blank). I also had to play with selecting contacts in order to figure out how to use it best. Once I experimented and figured it out, it works just great. It does exactly what I want it to do: exports to Excel my text messages (and even my emojis) with dates and times. The only improvement I could suggest would be the ability to choose multiple (but not all) contacts for export.
80sgal1 about Export SMS PRO - Text Exporter