You have to have one of these somewhere:

function MyClass()
{
  this.UpdateEditorFormValue = function()
  {
    for ( i = 0; i < parent.frames.length; ++i )
    if ( parent.frames[i].FCK )
    parent.frames[i].FCK.UpdateLinkedField();
  }
}
// instantiate the class
var MyObject = new MyClass();

And then before calling Form.serialize() you must call:

MyObject.UpdateEditorFormValue();

Then it will work