Hi,
If you inspect the <option> of the <select> you will find the value attribute has the ID of the list item.
You would have to use custom code (for example in dffs_PreSaveAction) to get the ID and write it to another field. You should be able to use code like this (written directly here so I haven’t tested it):
var selectedID = jQuery("#dffs_YourFieldInternalNameHere select").val();
setFieldValue("TheFieldYouWantToSaveTheIdIn",selectedID);
Alexander