On the plane...
On the island...
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The Female anchor is a character in Season 4, portrayed by Jill Kuramoto, who reported on the discovery of Flight 815 in the Sunda Trench.
She was first seen anchoring the news report at the beginning of the episode concerning the finding of the wreckage, which was watched by Daniel Faraday and his caretaker. She later reported on the recovery and identification of Seth Norris, which was watched by Frank Lapidus. ("Confirmed Dead")
Michael also saw her report on the discovery of the wreckage from his apartment in New York as he was trying to kill himself. ("Meet Kevin Johnson")