I don't know how much was shared with him about everything after that. You're welcome to fill him in, if you're so inclined. I doubt he'd want to hear it, though.

[Obi-Wan has to know some of it, either from Luke or someone from Ben's time, but she never asked just how much he knew. As she continues, as with before, her tone is kept as even as possible given the subject matter, but once again, the temperature rises. She may not be talking about what Vader had done to her specifically, but even thinking about him in abstract is enough to bring forward that anger and hate she feels for him.]

Darth Vader was one of the people closest to the Emperor. There was no length he wouldn't go to in order to carry out his missions, though I assume you've already guessed as much.