We have applied our empirical-PSF-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 right 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 Msun CO-core DA objects) while the red WDCS hosts the end-products of the He-rich population (~0.46 Msun objects, ~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.