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In the film Star Wars: The Force Awakens we learn that Kylo Ren

Is Anakin Skywalker's grandson, his predecessor

We also learn that he was trained by

Luke Skywalker

Surely his master would have told him about his predecessor, how he was seduced by the Dark Side and how he eventually returned to the Light Side of The Force?

And yet we hear him say he wants to finish what his predecessor started.

What does Kylo Ren know?