To move a task or task list from one project to another, just use drag and drop. Click on the task or task list you want to move. Hold down and move the mouse at the same time, then release the mouse where you want your task or task list to appear.
This allows you to move a task or task list to another project. Drag it to the name of the destination project in the menu bar on the left.
If you want to keep a duplicate in the original project, you can also duplicate the task or list and only move the copy.