Per the novel Out of the Darkness, they learned it in 2278 when David Sheridan II, possessed by a Keeper kept in an urn Mollari had given his parents, awoke and compelled him to journey to Centauri Prime. When John and Delenn travel there to rescue him, they are captured by Mollari. In the novel (from the Keeper link)
Garibaldi went to Babylon 5, where he was able to learn from Vir Cotto that the Drakh had been on Centauri Prime for quite some time, and that they were in control of the Emperor and Prime Minister.
Even if we discount the novel, War Without End Part 2 more or less implies they know about the Drakh by then, and older Delenn states that their son (David) is safe (meaning the Keeper was removed or at least discovered).