I use Scrum, not Kanban but I found this on the support site here:
Navigate to the backlog of the agile team.
Select the stories you want to move to an iteration or Kanban board, then click More > Move to . If moving the story to a Kanban board, the Move Story to the Kanban Board is displayed. If moving the story to an iteration, the Move Story to an Iteration dialog box is displayed.
Do either of the following:
For Scrum teams: In the Select Iteration field, select the iteration where you want to move the stories.
For Kanban teams: In the Select Kanban Board field, select your team Kanban board. (Kanban teams can have only one Kanban board.)
Click Move Story .
Katherine Haven, PMP VP, Director, Business Technologies - PMO FCB