Within Teamwork Projects, if you are an administrator, you can change the Date Completed information on a task.

Click the completed task name to go to the Task Details screen. In the left panel, you will see a Modify link next to the Date Completed.

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You can choose a new completed date here, as well as the person who created the task, and the person who completed it.

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Click Apply Changes to update the task information

For more information, see: Changing the creator of a task