I have written a simple add-on that will allow you to set the source and destination forums, and then once a week (on Sundays) all closed threads in the source forum will be moved to the destination forum.
Download the attached .XML file and then follow:
AdminCP ► Plugins & Products ► Manage Products ► Add/Import Product.
Click on "Choose File" and browse to the product .XML file that you downloaded.
Click "Import"
Next, set the options for the product and let me know if this does everything you need.
edit: I have uploaded an update which rebuilds the forum counters...which I initially failed to take into account