Arthur Zimmermann had no idea that "Blinker" Hall had read his secret message. But now that Hall had read it, what could he do with this information? On one hand, he believed that President Wilson, faced with the information in the telegram, would declare war on Germany. On the other hand, to share the telegram with Wilson would surely alert Berlin that the British had been reading their secret messages. As he walked back to his office, Hall considered ways that he could share the intelligence in the Zimmermann telegram and establish its authenticity without letting Berlin know that Room 40 had intercepted and read hundreds of their secret messages.

Why was Hall concerned that the Germans would learn about the British reading their secret messages?

The Germans would begin reading British secret messages to get revenge.
Reading an enemy’s secret messages is against the codes of war.
The Germans would then find a different way of transmitting their messages.
This knowledge would make the Americans sympathize with the Germans.