dude, that was so made up for the movie. that's not even a real theory. it was just to make Joker more relevant to the movie.
But he's not supposed to know he has a son. From the looks of the photos we've seen, I think Anakin never said jack squat about the saber. The one in the pics of him fighting Obi-wan in the Insider, as well as the new pic released in Hyperspace, he has that hilt that Obi-wan gives Luke but with a red blade. Based on what we've heard about where Anakin is when he turns, he doesn't have time to make a new saber, Palpatine probably gives him a new crystal (or whatever colors it, since we don't TECHNICALLY know, right finiti? yerrssot? just thought i'd add that to stop any possible fights). Anakin probably wouldn't bother making a new one anyway since its clear he's fond of that design. The three hilts we've seen Ani/Vader use are all basically the same design with just slightly different parts and colors. So I think Obi-wan will recover the saber after the fight for whatever reason, then switch the blade color back to blue, might make an iteresting last scene, but I don't think it would be something we need to see to get. But its clear Anakin did not know he had a son until he heard Skywalker destroyed the death star.