CT Did Obi-Wan know Vader lived prior to their meeting on the Death Star?

You meant Vader was alive, no ?

Cause from ROTS, he knows Lord Vader = Anakin Skywalker...

 

I would imagine he would have heard the reports of Vader and figured out who it was.

 

I don't see how Obi-wan COULD know that Vader is alive. Once he's on Tatooine, Obi-wan has no contact from Yoda, the Organas, any surviving jedi, the rebellion, nor the outside world in general. He can't go anywhere or do anything without attracting the attention of the Empire and he just witnessed Vader burning to death on Mustafar. The chances of Vader's survival by then is zero so as far Obi-wan is concerned, Vader is dead until he sees him again in ANH.

 

Even Tatooine gets HoloNet reports - and Ben can't spend all his time in the desert - he has to travel into town sometime to get appropriate supplies.

There's also the "training from Qui-Gon" bit - Qui-Gon has the opportunity to keep Obi-Wan informed about the most relevant facts.

 

The Force did it.