When it's time to end a message conversation, click on Close Conversation.
Then the thread disappears from the system. The participant can see that the matter is closed at the bottom of the conversation and no longer has the ability to write in the thread.
If you want to view your message history, go to Messages and then History in the extended left menu.
The history is stored for the same duration as other information in the system. You can filter messages within a specific time period or search by the participant's social security number. To read the message, click on it in the results list.