Vader conceivably could have kept Kenobi’s saber on his person, therefore it survived DS 1 blowing up. After that, who knows?
Well the Kenobi lightsaber prop was re-tooled for Luke’s lightsaber, so now I’m imagining a Rogue One type story between Empire and Jedi where Luke steals Ben’s lightsaber from Vader and improves it, since he lacks the skill to make one himself.
Luke built a new green saber. (It was even a cut scene from the movie.) Vader even referred to it as a sign Luke’s skills were complete.