In Episode III (final battle), we can see Kenobi vs Vader (Anakin) and two white lightsabers. After he defeats Vader, Kenobi takes Vader's.
Darth Vader does not seem like the type of man to keep ornaments/trophies himself. What happened to Obi Wan Kenobi's third lightsaber?.
During his years as a Jedi, Obi-Wan Kenobi fought with three lightsabers. His first had a green plasma blade and a hilt similar to that of his master, Qui-Gon Jinn. After attaining the rank of Jedi Master, Obi-Wan built a third saber, also with a blue plasma blade. Star Wars Build your own Obi-Wan Kenobi Lightsaber toy & Luke Skywalker Lightsaber toy @ Disneyland