Within Teamwork.com, you can move messages to another project on your site.
Go to the Messages area of your project and select the message you wish to move.
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Once you are viewing the individual message, click the options button (three dots) to the right of the message and select Move Message from the dropdown menu.
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In the move message modal, you can select the destination project for the message.
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Note: Only project admins and site admins can move messages between projects. Project admins can only move messages to other projects where they are a project admin.
For more information, see: Adding a New Message