Withing Teamwork Desk, when creating a trigger there is the option to apply it to all inboxes or a few inboxes.

To enable this on existing triggers or new triggers, click on the your profile icon to the top right of the navigation bar and select 'Settings':




Near the top of the page select the 'Inboxes' area of settings:


Select the inbox which has the trigger you wish to edit and select triggers from the left pane:

 

When you are editing or creating a trigger you can apply to all inboxes from the summary area of the trigger setup:



For more information see: Editing or deleting a trigger