JQuery UI use sortable without sorting, just move

You don't want everything to be sortable for this.

The <li>s in the top list should be draggables with helper: 'clone', this helper option lets you drag copies of the <li>s out of the list without altering the list itself. So you start with this:

$('#list-A li').draggable({
    helper: 'clone'
});

Then you need to make the bottom list droppable and you want to clone the elements when they're dropped. You can do the cloning using the drop event:

$('#list-B ul').droppable({
    drop: function(event, ui) {
        $(this).append($(ui.draggable).clone());
    }
});

You want to be able to move things around in the bottom list and that's where sortable comes in. So the bottom list should be sortable as well as droppable. You also have to keep the droppable from cloning things while you're only sorting them. You can use the start and stop sortable events to set a data flag and then check that flag in the droppable drop event handler. Something like this for the sortable:

$('#list-B ul').sortable({
    start: function(event, ui) {
        ui.item.data('sorting', true);
    },
    stop: function(event, ui) {
        ui.item.removeData('sorting');
    }
});

and then add a check to the drop event handler:

$('#list-B ul').droppable({
    drop: function(event, ui) {
        if(ui.draggable.data('sorting'))
            return;
        $(this).append($(ui.draggable).clone());
    }
});

Demo: http://jsfiddle.net/ambiguous/PyWAM/