Did anyone else notice that the BBC tarted up their headline to the point that it's actually false? The piece of paper was written by the Germans. It didn't "fool" them. It was proof that the Germans had been fooled, but I guess that's not quite as good for linkbait.
If you have broken the enemies crypto AND he doesn't know you have - then you can also send fake messages which they are going to believe.
So the Brits could have sent a message ordering a few panzer armies from Normandy to the Pas de Calais. It doesn't seem that this was ever done - presumably because it gave the game away.
Even more interestingly - the Brits kept secret that they had cracked enigma into the 1980s because after the war they distributed the 'uncrackable' German code machine to lots of rather gullible allies
