Upvote:2
Without formal diplomatic channels for a direct communiquΓ©, the Western Allies delivered the message indirectly, while the Soviets found a more direct method of delivery...
The Western allied powers published the declaration in the public press (freely available to Axis spies in the UK and the US who could then easily transmit this back to their contacts in the Third Reich). The Axis powers also monitored the Allied news reports to glean intelligence from them (newspapers and newsreels were available through foreign offices and agents in neutral nations as well as embedded in the US and UK).
According to this JSTOR History Journal Article (Vol. 76, No. 248 (October 1991), pp. 401-417) the Moscow Declaration was published:
Source: JSTOR
As proof that the Moscow Declaration was published, I found these three New York Times archived articles from 1943:
A basic search of the British Newspaper Archive turned up several results (many of which do not apply, but several indicate publishing various articles about the declarations from 1943 through the end of the war, and after):
The tribunal heard the case against four defendants, one Soviet collaborator and three Germans, members of the Wehrmacht, police, and SS forces, respectively. They were charged both under the Soviet and international law, the Moscow Declarations. The defendants were accused in participating in the murders of Soviet citizens, while the collaborator was charged with treason. [emphasis added]
The National Library of Australia includes this archived news report from The Argus (Melbourne, Vic. : 1848 - 1957), Tue 21 Dec 1943, Page 12, RUSSIANS SEE HANGING OF TORTURERS, covering the trial and hangings:
Before a crowd of 40,000 the 3 Germans and one Russian, who were convicted by a military tribunal of having taken part in mass extermination of Soviet citizens, were hanged in the snow-covered public square in Kharkov yesterday.
The condemned men were Reinhardt Retzlav, 36, of the German field police; Hans Ritz, 24, formerly assistant commander of Gestapo in Kharkov; Capt Wilhelm Langheld, 52, of the German military secret service; and Michel Bulanov, a Russian who served the Germans as a motor-driver.
Foreign correspondents who had been flown from Moscow to see the conclusion of the trial, saw the execution...
Upvote:3
There was communication between the sides via neutral countries. The concept of the "Protecting Power" is important here: When states break off diplomatic relations, they appoint some other state to look after their diplomatic property and provide a channel for communications.
During WWII, Switzerland and Sweden acted as protecting powers for many countries. So the Moscow Declarations could have been communicated to the Swiss Foreign office in Bern, Switzerland, via one or more of the declaring powers' embassies in Bern, Switzerland. The Swiss Foreign Office would send that message, in the Swiss diplomatic code to the Swiss Embassy in Berlin, who would then hand it to the German Foreign Office.
Source: A rather good reddit thread, quoting an article on the website of the International Red Cross.