Within Teamwork, you can move or copy a task list to another project on your site, or make a copy of it in the current project.
Hover over the task list name and click the three dots to the right. Select the Move or Copy option from the dropdown menu.
In the copy/move modal, you can choose whether you want to copy or move the task list, and pick a destination project.
You can use this option to copy all task lists from one project to another if you would like to combine two separate projects.
Copying a task list
When copying a task list, you can choose whether you want to include completed tasks in the copy.
Comments and time logged will not be copied.
Moving a task list
When moving a task list to another project, all comments and time logged on the tasks will also be moved to the new project.
If a task being moved is assigned to a person who is not a member of the target project, the task will be re-assigned to Anyone.
For more information, see: Creating a Task List