Canon
Eu não acho que há uma resposta no cânon. O sabre de luz de Obi-Wans foi deixado quando Vader o matou. Pode ter sido destruído na explosão da Estrela da Morte, ou Vader ou alguém pode tê-lo tomado (como em Legends), mas seu status de canon após New Hope é desconhecido.
No entanto, há uma resposta do Legends.
Legendas
Em Legends, Vader realmente manteve o sabre de Obi-Wan como um troféu.
“Darth Vader…,” Luke said.
It surprised him that Darth Vader would want to keep the lightsaber of his former teacher, but it wasn’t impossible. Vader could have sent it away from the Death Star just after he defeated Kenobi. Or he might even have taken it with him when he escaped the destruction of the Death Star.
—Junior Jedi Knights: Vader's Fortress
Mais tarde, Luke a recupera.
“It’s good to have you back, Artoo,” Luke said. “From all the excitement, I take it you found the lightsaber.”
“And more,” Tionne answered, holding out the Holocron for him to see. “Master Ikrit has the lightsaber with him.”
—Junior Jedi Knights: Vader's Fortress
Um personagem secundário chamado Orloc tenta roubá-lo mais tarde, mas não consegue :
"You would have killed my friends—and maybe even me—just to keep the Holocron and Obi-Wan Kenobi's lightsaber. You thought they could give you true power, just like I believed you could give me real power. The power of the Force is real. But you knew you never had it. I was the fool."
—Junior Jedi Knights: Kenobi's Blade