We have applied our empirical-point-spread-function-based photometric techniques on a large number of calibration-related WFC3/UVIS UV-B exposures of the core of omega Cen, and found a well-defined split in the bright part of the white-dwarf cooling sequence (WDCS). The redder sequence is more populated by a factor of ~2. We can explain the separation of the two sequences and their number ratio in terms of the He-normal and He-rich subpopulations that had been previously identified along the cluster main sequence. The blue WDCS is populated by the evolved stars of the He-normal component (~0.55 M &sun; CO-core DA objects), while the red WDCS hosts the end products of the He-rich population (~0.46 M &sun; objects, and ~10% CO-core and ~90% He-core WDs). The He-core WDs correspond to He-rich stars that missed the central He ignition, and we estimate their fraction by analyzing the population ratios along the cluster horizontal branch. Based on archival observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555.