Upvote:3
You can exit to wherever you want. It's perfectly possible to enter from a third country to a given Schengen country and leave from another Schengen country to yet another third country. No matter where you go or where you exit, you should get an exit stamp, documenting the time you spent in the Schengen area.
Incidentally, Zambia cannot grant you a Schengen visa, only (the consulate of) a Schengen member state can. In principle, you have to be a resident in the relevant area to apply to a given consulate. Hopefully your status in Zambia won't be an issue but that's probably more of a problem than leaving to the US.