According to Plato the Greeks didn't knew of this story. The first Greek to learn about Atlantis was Solon, who stayed for some time in Egypt.
The story says that a wise Egyptian priest told Solon that there had been numerous cataclysmic natural disasters in the past, each time exterminating most of humanity. And that because of that, after the disasters humans would start building their civilizations once again from zero, having lost all of their knowledge. So the Egyptian priest tells to Solon that the Egyptians were wise to write history on the walls of their temples. Thus with ink that is waterproof they wrote on stone buildings that are fireproof and earthquake proof, in case yet another disaster happened, the history wouldn't be lost. (Think about all the hieroglyphics written on the walls of the Pyramids...)
So eventually the priest says that a cataclysmic event did happened, and that lead the Greeks, who weren't prepared to loose their knowledge about the past, while the Egyptians retained it. And he goes on to tell one of the stories written on the walls to Solon, as an example. And that story, is the story of Atlantis.