First, you cannot close a fiscal year twice in Dynamics GP. Second, if you want to create a 13th period, the start and end dates should be the same - December 31, for instance.
So, you cannot setup a 13th period after closing the fiscal year. You would want to do that before closing. Period 12 would begin on 12/1 and period 13 would begin on 12/31. That would limit transaction dates for period 12 to 12/1 thru 12/30 and period 13 to 12/31 thru 12/31.
If you need to setup a period 13, you'll also need to reconcile Fiscal 2013 periods.
Hope this helps.