We report experimental investigations of spin-to-charge current conversion and charge transfer (CT) dynamics at the interface of the graphene/WS2 van der Waals heterostructure. Pure spin current was produced by the spin precession in the microwave-driven ferromagnetic resonance of a permalloy film (Py=Ni81Fe19) and injected into the graphene/WS2 heterostructure through a spin pumping process. The observed spin-to-charge current conversion in the heterostructure is attributed to the inverse Rashba-Edelstein effect (IREE) at the graphene/WS2 interface. Interfacial CT dynamics in this heterostructure was investigated based on the framework of the core-hole clock (CHC) approach. The results obtained from spin pumping and CHC studies show that the spin-to-charge current conversion and charge transfer processes are more efficient in the graphene/WS2 heterostructure compared to isolated WS2 and graphene films. The results show that the presence of WS2 flakes improves the current conversion efficiency. These experimental results are corroborated by density functional theory (DFT) calculations, which reveal (i) Rashba spin-orbit splitting of graphene orbitals and (ii) electronic coupling between graphene and WS2 orbitals. This study provides valuable insights for optimizing the design and performance of spintronic devices.