After the events of A New Hope, Sidious believed Obi-Wan was dead. Vader apparently never told Sidious that Obi-Wan disappeared instead of being sliced in two on the original Death Star.
From the 1983 novelization of Return of the Jedi by James Kahn,
“Tell me, young Skywalker,” the Emperor said when he saw Luke’s first struggle had taken its course. “Who has been involved in your training until now?” The smile was thin, open-mouthed, hollow.
Luke was silent. He would reveal nothing.
“Oh, I know it was Obi-Wan Kenobi at first,” the wicked ruler continued, rubbing his fingers together as if trying to remember. Then pausing, his lips creased into a sneer. “Of course, we are familiar with the talent Obi-Wan Kenobi had, when it came to training Jedi.” He nodded politely in Vader’s direction, indicating Obi-Wan’s previous star pupil. Vader stood without responding, without moving.
Luke tensed with fury at the Emperor’s defamation of Ben — though, of course, to the Emperor it was praise. And he bridled even more, knowing the Emperor was so nearly right. He tried to bring his anger under control, though, for it seemed to please the malevolent dictator greatly.
Palpatine noted the emotions on Luke’s face and chuckled. “So, in your early training you have followed your father’s path, it would seem. But alas, Obi-Wan is now dead, I believe; his elder student, here, saw to that—” Again, he made a hand motion toward Vader. “So tell me, young Skywalker—who continued your training?”
And from the script for The Empire Strikes Back:
Emperor: We have a new enemy - Luke Skywalker.
Vader: Yes, my master.
Emperor: He could destroy us.
Vader: He’s just a boy. Obi-Wan can no longer help him.
Vader would say the Obi-Wan can no longer help Luke because he probably believes Obi-Wan is dead. Yet, he should not assume his previous master was dead because of what Obi-Wan told him a moment before his "death".
Obi-Wan: Strike me down and I shall become more powerful than you can possibly imagine.
For somebody to disappear was a trick Vader had never seen before. To the best of my knowledge, it was a trick nobody in the galaxy had ever seen before since Obi-Wan was the first to will his body into becoming one with the Force. (Qui-Gonn was a Force Ghost, but his body did not disappear as Obi-Wan's did. And according to Lucas, "We never see the ghost of Qui-Gon; he's not that accomplished. He's able to retain his personality, but he's not able to become a corporal ghost.") Nor was there anything in the Jedi teachings about Force Ghosts. It would puzzle, perhaps even unnerve, Vader.
Did Vader deliberately hide this from his master? We know Sidious could so easily extract information from the minds around him, so hiding such a crucial piece of knowledge would be difficult.
What exactly did he tell Sidious?
I am looking for answers from G-canon or T-canon, not lower canon levels.