It was very clear from the last book that the Cloak which Harry possessed was the original Invisibility Cloak and the Hallows do exist.
“The Hallows, the Hallows,” murmured Dumbledore. “A desperate man’s
“But they’re real!”
“Real, and dangerous, and a lure for fools,” said Dumbledore.
“So it’s true?” asked Harry. “All of it? The Peverell brothers—”
“—were the three brothers of the tale,” said Dumbledore, nodding.
You have guessed, I know, why the Cloak was in my possession on the
night your parents died. James had showed it to me just a few days
previously. It explained so much of his undetected wrong-doing at
school! I could hardly believe what I was seeing. I asked to borrow
it, to examine it. I had long since given up my dream of uniting the
Hallows, but I could not resist, could not help taking a closer look .
. . It was a Cloak the likes of which I had never seen, immensely
old, perfect in every respect.
Deathly Hallows, Ch 35: King's Cross
Also, Xenophilius made it very clear when the Trio goes to meet him that there are Invisibility Cloaks available in the market but there is only one "true" Hallow.
“Ah, but the Third Hallows is true Cloak of Invisibility, Miss
Granger! I mean to say, it is not a traveling cloak imbued with a
Disillusionment Charm, or carrying a Bedazzling Hex or else woven from
Demiguise hair, which will hide one initially but fade with the years
until it turns opaque. We are talking about a cloak that really and
truly renders the wearer completely invisible, and endures eternally,
giving constant and impenetrable concealment, no matter what spells
are cast at it. How many cloaks have you ever seen like that, Miss
Deathly Hallows, Ch 21, The Tale of Three Brothers
So i guess the Cloak which Moody possessed was one which was charmed or made from a special material. The fact that such Cloaks existed was not really news.