This might sound stupid but if you or the neighbour has a digital camera take a close up of the broken bit and a reasonable close one of the whole thing and take the camera [or picture copy if you can load it on a PC and print it out] to the nearest plumbing shop and they will most likely have the part or tell you where to buy it.
I did, they did laugh though but thought it was a very good idea and better than trying to do an abortive drawing.
Take the pictures at various angles untill you clarify you can see what the part is clearly. delete all unwanted cistern pictures so the picture search is easy
Bob
Bob
November 2005