Eloise Hawking gives Jack Locke's suicide note, further instructions

Jack goes with Eloise Hawking to her office where she tells him that what she has to say doesn't concern the others. She looks under papers on her desk and pulls out an envelope with Jack's name on it. She tells him that it is Locke's suicide note and that he hung himself. She says that there are probably a lot reasons why Locke would kill himself but that Locke is going to help Jack get back to the island. Locke's body will serve as a proxy for Christian Shephard's body. She tells Jack that he needs to recreate the conditions of the original flight and that he needs to give Locke something that belonged to Christian. At this point, Jack is still playing the role of the "man of science" and fights Ms. Hawking's instructions saying they're "ridiculous." She tells him to stop thinking about how ridiculous it seems but to ask himself "whether or not you believe it's going to work." She continues by saying "That's why it's called a leap of faith Jack."

In this scene, we see Jack's hardlined lack of faith become even more maleable as Eloise Hawking breaks things down for him. You can tell at this point that he's still not completely convinced yet though.

So how did Eloise Hawking end up with Locke's suicide note for Jack? There's also still the question of how she knows and understands what steps need to be taken to get back to the island? She is indeed a mysterious character.