No, the electrons actually move in the same direction always, just as a free falling object always moves towards the locally dominant mass. We could call the direction of electron movement "right".
We tell the aliens: you take all sorts of organics with liquid inside (on earth we typically use a lemon, but other organics will do), and put a stake of element 29 in one side and a stake of element 30 in the other. You then connect them with a length of element 29. Keep trying different organics until you find one that works. They might not have lemons, but there is a good chance that something will eventually work.
You'd need to predefine what the atomic numbers mean and some other things, but we're already assuming some level of communication already being established so this aspect is not far-fetched.
See the problem? :)
Edit: if you make the electron move, it will move towards or away from the wire, depending whether it's moving in the same or opposite direction as the electrons in the wire.
Remember you haven't yet established with the alien what you mean by right and left, so you won't be able to instruct it to set up your apparatus rather than its mirror image, and of course you can't appeal to the right-hand rule.
This problem has no solution because electromagnetism is right-left symmetric. You would need to use the weak decay (and assume that your alien is made of matter rather than antimatter)