How to pull a report in rtc to get all the stories which moved to next iteration

I'm not sure if this is the best way, or if it matches your expectation, but.. you can obtain a list of all the stories which are Planned For a particular iteration.

E.g. create a simple work item query to obtain these work items
Work Item Type = Story
Planned For = [iteration to which the stories were moved]

Then you can display the query and export that using the Download as Spreadsheet option (csv).

You can display the result in the dashboard using the Work Items widget.

Otherwise, there are many BIRT reports and dashboard widgets that may be relevant..

For example, I found a "Deferred Work Items" report. This shows the below:



Is this the kind of thing you are looking for?