I have an S4 with the latest software update (though this has been a problem for a long time before too). And when I am in a group text with Iphone users, it seems that my outgoing texts get stuck in limbo until all of theirs is through. Sometimes several minutes, so I am always behind in the conversation. Is there a fix?
Even I own a galaxy s4 and I know that the latest update has been so terrible. I don't think that Samsung is anyway going to push any updates for this but follow the solution below.
You can wipe the cache partition from the recovery mode. (Shut down and reopen by pressing menu, power and volume button at once) then scroll down using volume button to wipe cache partition and power button to confirm. Reboot the device.
Very important go to developer options and switch off all the animations.
Follow some more from. http://www.androidpit.com/galaxy-s4-lollipop-problems-and-how-to-fix-them
What messaging app are you using? People experience a lot of variation depending on the app. I think even Samsung will allow you to change your default texting app. May I suggest Google's very own Messenger? Link It's supposed to have pretty good group messaging support.