Thanks Jake!
Had a look at the jsfiddle editor - it seems to me, that this use-case breaches its capabilities, because I would need both a source and target page.
Yes, the ID (or ideally elements in general) in both parts are the same.
$.cache1 holds the entire target page as a DOM representation.
However, the elements in question are identical from their "location" in the DOM even if their values / content might be different.