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 4.3x4.3. 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 clusters 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.
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