This feature is available in all editions.
You can move a task or test to another story by selecting a new 'parent' for it.
Option 1: Edit Task Details
Edit the task, and then click the magnifying glass icon next to the parent workitem on the Edit Task page.
On the resulting popup page, find the new backlog item
Use the Select link on the right to select a backlog item
Save your changes on the Edit Task page
- The task has now been assigned to a new backlog item.