Here is an example double list thing: http://jsfiddle.net/xhdUW/
If one of the parent lists already has content, the list items will transfer between the parent lists easily. But if one of the parent lists is empty, the list items will not go into the empty parent list.
The docs on .sortable say that transferring to empty lists should be enabled by default: http://jqueryui.com/demos/sortable/#empty-lists , though, even when I specify dropOnEmpty: true, I get the same behavior.
Your empty list have no height and no vertical padding.
Try to add something from list:
padding-top
padding-bottom
min-height