Well, first, you figure out what part of the code determines whether or not you are an admin, and then you copy the code into the clone website (I am actually uncertain as to how to make the clone website...) and then you mess with the code on the clone page so that the clone page thinks you are an admin, and then you act like the clone page is real, and you actually do have admin powers, and because the code of the clone page has the authority to actually change things, and the computer doesn't see anything wrong, because you didn't edit the original page.
however, I think I would need to see the HTML code of this page from an Admin's perspective before I could actually do anything. I also would probably need to find the code behind the HTML code, but HTML is where everything runs from, so I think that if I trick the HTML code, then the HTML code will trick everything else.
Honestly, all of it is "theoretically possible," probably the same kind of "theoretically possible" that is in a lot of WoBs. Meaning, it might work, but it would be really hard to make it work.