You can delete any conversation from your messenger, either because the conversation is over or because you no longer want to display it in your messenger.
To do this, please go to the conversation’s details in the messenger and click on the trash can icon 
or the 3 dots on the mobile app 
and confirm the action for it to be completed.
Once deleted, the conversation will no longer show up in your mailbox. However, if the contact writes to you again, the conversation will be become available.