Ellie in the episode Jughead is actually a young eloise hawking. Fits as Ellie is an abreiviation of Eloise. When she meets Daniel Faraday, and he tells her he is from the future, this sparks a fascination in her of time travel, and Daniel as he simply disappeared. She then has a baby with Charles Widmore, and names the baby... Daniel Farraday! Then when Charles is banished from the island by the others, she leaves with Charles and the baby. Once they leave, they don't know how to get back. She then dedicates her life to the study of time travel and the island, and teaches her knowledge to Daniel also. Charles also pays for Daniels research. Then Daniel leaves with the freighter to find Ben, and disappears. This is what leads her to locate and maintain the Lamp post station, to find the island, and Daniel. It seems at this point in her life her and Charles have split up, but i believe they are on good terms still. Ms. Hawking told Charles where to put the cameras in tunisia from the research at the lamp post station. Finding the island isn't the stations only use, it also locates the other 'pockets of electromagnetic energy' as she told Jack in 316. That specific place in the Tunisian desert is one of those places, and she knows Locke will appear there. She tells Charles this, which leads him to put cameras there so that he knows when get him from the desert. Her main care is for the future of the island, like Widmore. Therefore she is using Ben to get the Oceanic 6 back to the island, while leaving the more important task of getting Locke back to Charles. Maybe Ben knows she is using him, or maybe she told him that she is no longer with Charles, which made Ben trust her. In Desmonds flashback where he is going to stay with Penny, Ms. Hawking turns up to make sure he leaves her and goes to the island because as Daniel put it in Because you left, he is special, and the rules don't affect him. If he changed him fate like he was close to doing, he wouldn't have gone to the island, killed the person pushing the button (kelvin) left the button for too long resulting in oceanic 815 crashing, which was meant to happen! Basically, if he stayed with Penny, Kelvin would have carried on pushing the button and 815 wouldn't have crashed. The way she knows that Desmond time travelled was because the island appeared when he turned the failsafe key at the end of season 2. (Penny's station in the arctic) The resulting implosion from not pushing the button would have killed him, however the effect of turning the key is to make the island send anyone in the station to a safe place. Locke and Eko appeared in the jungle, Desmond back in time, saving them from the implosion. Hawking also knew that turning the key would result in the island becoming visible briefly, so in 2004 when it appears (after turning the key) she saw where the island appeared, and calculated when and where whoever was in danger would be sent from those co ordinates by use of the lamp post once again, thus, her visit to Desmond.