Hello and welcome to Android Forums!
I am not sure how far you have gone for troubleshooting this issue but here are my suggestions. Try installing Go SMS pro from the play store and see if this helps, if not try clearing the cache and clear data from the messaging app on the phone. if either of these do not help try doing a factory reset. There are some other things that could play into this, are you on a non stock ROM?
Hope this helps, if not please re-post a message in this forum or join and we can continue this thread.
Willis