What is Dr. Yu Tsun’s purpose in the story? What is his mission and does he achieve it?

Dr. Yu Tsun is the narrator of Jorge Luis Borges's "The Garden of Forking Paths." The text opens by stating the following:

The following deposition, dictated by, read over, and then signed by Dr. Yu Tsun, the former teacher of English as the Tsingtao Hochschule, casts unsuspected light upon this event.

This sets up who Dr. Tsun is and what his part in the story is as well. The curious thing about Dr. Tsun acting as the narrator is that the text functions as Dr. Tsun's deposition regarding the murder of Dr. Stephen Albert, whom he (Tsun) murdered.
In regards to his "mission," Dr. Tsun is a German spy. His mission is to get word to the Germans about the war. He decides to murder Dr. Albert so that he can use the murder to relay information to the Germans rather indiscreetly, through the newspaper. By murdering Albert, the news of his death will be connected to Dr. Tsun openly, which keeps his cover as a spy undisclosed. Although Dr. Tsun is caught and is scheduled to die by hanging, he was successful at getting the information regarding the city which will be attacked to the Germans. The name of the city is Albert.