Currently the way the system is setup when a staff replies on a ticket the end-user receives the Response/Reply Template. This also happens when the staff replies and at the same time closes the ticket. However, the message to the end-user is the same. We'd like to modify the reply template to specifically note that the ticket has in fact been closed. Is there anyway to do this?

There is no such thing as a Close Ticket Template in osTicket.  If the Agent is closing the ticket you can use a canned response during that last update.

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