Within Teamwork Desk you can use the collision detection feature to ensure that you and your fellow agents do not reply to the same customer at the same time.
Collision detection is turned on by default within your inboxes and will notify you when another agent is viewing or replying to a ticket.
When you and another agent are viewing the same ticket you will see their name above the ticket information:
When an agent has already started to reply to a ticket that you enter then you will see a red band to the top of a ticket notifying you of this:
For more information see: Creating and using canned responses