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Impressions before reading: My immediate reaction to the promised "Neil Armstrong meets Luna" is not particularly positive; while it seems like a fine premise for a joke, I don't know that there's a story to be had there. Especially not in 1500 words. On the other hand, that might be short enough to just be a joke, which would be a perfectly acceptable thing. I'll try to calibrate my expectations to what I'm given.
Zero-ish spoiler summary: When the Apollo 11 module sets down on the surface of the moon, they find a purple "unicorn" on the surface.
Thoughts after reading: The author him/herself describes this as "just a silly little oneshot of simply 'Neil Armstrong meets Luna.'" And that's a perfectly fine thing to write and share! But even within that context, there are a lot of problems with The Eagle Has Landed.
First, and most obviously, there's no actual plot. Armstrong and Luna come face-to-face, Houston tries to scramble a plan, the end. There's no arc, no resolution, and not even a suggestion of how the lunar expedition might conclude. This may well be addressed in the sequel, but in that doesn't give this piece any more of a sense of completeness or closure.
Second, the story is dotted with factual errors, incomprehensible leaps of logic, and odd interruptions. It states that there was no plan for if the Apollo astronauts encountered alien life; control magically intuits that Neil and Luna will be able to hear each other speak if they touch their heads together; the story breaks out a parenthetical to let us no that the Capsule Communicator is abbreviated to CAPCOM, a title it never uses again. And these are only three representative samples of the dozens of such issues which fill this very short fic. There literally aren't a half-dozen sentences in a row at any point in the story which don't have at least one questionable decision or inclusion of some sort.
★☆☆☆☆ (what does this mean?)
Also, I think it's a mistake to start a fic--really, any fic--with Armstrong's iconic “That's one small step for [a] man... one giant leap for mankind.” Whether you put the "a" in there or not, a significant fraction of readers will think you've misquoted him, which isn't really an ideal reaction to a first sentence.
Recommendation: Although it's not offensive or otherwise irredeemable, I still can't think of any group that I'd actually recommend this story to.
Next time: There, They’re…, by FanNotANerd