Okay, I actually forgot that I asked for a part number, but now that I found my own post, I guess I should supply an update.
After a second e-mail, in which I said I did not have a part number for just an arm, Playmobil (New Jersey) sent me a whole troll.
I sent a nice letter thanking them, and sent them the poor troll with the two right arms.
Problem solved and a still very happy and satisfied Playmobil collector. Now if I could just find a purple troll on Ebay!