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Trivia: Moses Ingram received racist attacks and death threats from overzealous fans for her role in this series. Lucasfilm actually warned her prior to signing onto the series that she would likely be the target of vitriol from racist fans, following similar attacks on John Boyega and Kelly Marie Tran.
Question: How can Obi-Wan believe that Anakin died after their fight on Mustafar? The movies make it clear that a Force-user can feel when a close friend or loved one is still alive, or is in pain. Yoda even sensed that Anakin was in "terrible pain" after Anakin turned, and Obi-Wan had a closer friendship with Anakin than he did.
Answer: He believed Anakin died. Anything he felt for him, he believed was just memories, sadness, and guilt for his friend. An emotional feeling filled with pain. Plus, Anakin did die. Only Darth Vader lived. A Sith Lord filled with hate and bitterness.