The State-of-the-Art HST Astro-Photometric Analysis of the core of
  $\omega$ Centauri. II. Differential-Reddening Map
  We take advantage of the exquisite quality of the Hubble Space Telescope
astro-photometric catalog of the core of wCen presented in the first paper of
this series to derive a high-resolution, high-precision, high-accuracy
differential-reddening map of the field. The map has a spatial resolution of
2x2 square arcsecs over a total field of view of about 4.3'x4.3'. The
differential reddening itself is estimated via an iterative procedure using
five distinct color-magnitude diagrams, which provided consistent results to
within the 0.1% level. Assuming an average reddening value E(B-V)=0.12, the
differential-reddening within the cluster's core can vary by up to +/- 10%,
with a typical a standard deviation of about 4%. Our differential-reddening map
is made available to the astronomical community in the form of a
multi-extension FITS file. This differential-reddening map is essential for a
detailed understanding of the multiple stellar populations of wCen, as
presented in the next paper in this series. Moreover, it provides unique
insight into the level of small spatial-scale extinction variations in the
Galactic foreground.
