Hi @Robroy1, welcome to our forum.
In the inbuilt Messaging application there is no setting to see if the counterpart has read the message or not, you can only see if it has been delivered. There may be other applications in the Google Play store that has this option, however I'm not sure if it is possible to have such an option for text messages.
If you search for "SMS application" or similar in the Google Play store, there will be some different applications that you can try.
Let me know how it goes!
