Models for the internal structure of the icy satellites Ganymede and Titan suggest that both moons are differentiated with a hydrosphere of ices and liquid water overlaying an inner rocky core. The presence of significant amounts of Insoluble Organic Matter (IOM) in this silicate layer has recently been advanced to properly explain the density and moment of inertia of these moons. The evolution of the IOM at the elevated temperatures (T ≤ 800 K) inside icy worlds could have a defining impact on their habitability and chemical evolution, including the formation of an atmosphere. However, the effect on these thermal reactions of the high pressures (P ≤ 10 GPa) found inside planetary environments remains largely unknown. We propose to use in situ powder and single-crystal X-ray diffraction (XRD), on diamond anvil cell samples of IOM and water, to establish a comprehensive picture of the fate of the primordial organic matter during the differentiation process in large icy moons.