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
Select the task which you want to move and click Edit.
In the Task window, click the magnifying glass icon next to the parent backlog.
In the resulting Parent Backlog window, choose the required new backlog item and then click Select.
Click Save in the Task window.
The task has now been assigned to a new backlog item.