The biggest issue with SMS is the Red notification number near the SMS doesn’t really tell you which SMS are “new”
It appears that the SMS window sorts by date, not by read / unread. Also only the “owner” of the SMS has the Green / Grey dots on the message to toggle the message read. A user might see 8 SMS notices, and have 200 messages, but no idea where the “8” unread ones are at.

All Possible Suggestions
Suggestion 1, Make Conversation boxes bold or highlighted to show there is an unread message in that conversation.
Suggestion 2, If message unread, put it at the top and sort by date. Put read messages also by date, but below/after the unread column.
Suggestion 3, click on the notice number the (8) and have it just load the 8 specific unread messages into the window vs all of them?
Suggestion 4, add for 'admin users' a 'See All' Toggle to enable seeing all SMS messages/notifications VS just their own SMS.
Suggestion 5, make a permissions level so the admin can see which users own which SMS, what has been replied to, etc.
TL/CG