Однако есть и такое свидетельство (речь идет о ноябре 1913 г.): "Учитель смотрел на Луну.
As a help for rockzmom and her daughter, here's my translation of this story:

[One could argue that Anna Vyrubova only invented Rasputin's "prophecy" about WWII after the war had already happened.]

However, there's also this testimony (the context refers to November 1913):

"The Teacher [Rasputin] was looking at the Moon. He said: "It's strange -- people are stupid, you know, but when they want something, they shall do it."

I asked him: "Who, Grigorii?"

And he said that the Americans would walk on the Moon, leave their disgraceful flag, and fly away. And I asked: "How is that? There's no air there."

He said, "They'll be in crates, and people here will be outraged that they surpassed us. US! But don't you fear -- we'll get there before them, and we'll be the first. It'll be Yuri."

And I asked: "First where? On the Moon? And which Yuri? You don't mean Duke Yuri Petrovich Izottsev?"
And he suddenly got angry: "You must've been born stupid! Not on the Moon, you silly hen, but first in the heavens! And not that duke of yours."

And after that we spent a long time praying to the Lord together."

Let's recall that Anna Vyrubova died in 1964, when the American "Apollo" program to be first on the Moon had not yet begun. [sic]

P.S. Strictly speaking, the "Apollo" program had been conceived on paper as early as 1960, and huge amounts of money and manpower began flowing into the project not long after Kennedy's public announcement in May 1961. So it's possible that Vyrubova made this claim after she'd heard that the US government was heavily committed to the Moon mission. However, it's also true that she died even before the Americans had manage to orbit the Moon (Apollo 8, in 1968), let alone actually landed and walked on the lunar surface.

P.P.S. Grammar question: Why are the verbs perfective past in вишь – захотели и сделали? I assume that a future action is actually intended here, as in Поехали! ("Let's go!"). Or is there some different rule at work?