We used optical images acquired with the Wide Field Camera of the Advanced Camera for Surveys onboard the Hubble Space Telescope and near-infrared data from GeMS/GSAOI to construct a high-resolution extinction map in the direction of the bulge stellar system Liller 1. In spite of its appearance of a globular cluster, Liller 1 has been recently found to harbor two stellar populations with remarkably different ages, and it is the second complex stellar system with similar properties (after Terzan5) discovered in the bulge, thus defining a new class of objects: the Bulge Fossil Fragments. Because of its location in the inner bulge of the Milky Way, very close to the Galactic plane, Liller 1 is strongly affected by large and variable extinction. The simultaneous study of both the optical and the near-infrared color-magnitude diagrams revealed that the extinction coefficient R$_V$ in the direction of Liller 1 has a much smaller value than commonly assumed for diffuse interstellar medium (R$_V=2.5$, instead of 3.1), in agreement with previous findings along different light paths to the Galactic bulge. The derived differential reddening map has a spatial resolution ranging from $1$ to $3$ over a field of view of about $90$X$90$. We found that the absorption clouds show patchy sub-structures with extinction variations as large as $delta {rm E}(B-V)sim0.9$ mag.