Spin-to-charge current conversion (SCC) by inverse Rashba Edelstein effect (IREE) has been recently observed by spin-pumping experiment in single layer graphene (SLG) placed on ferromagnetic substrate composed mostly of Ni. However, a prior angle-resolved photoemission spectroscopy (ARPES) shows a negligible Rashba splitting at Γ−M, unsupportive of SCC by IREE. In this work, using density functional theory with spin-orbit coupling (DFT + SOC) calculations, we obtained the Rashba-type spin-resolved bandstructure on relevant symmetric k-points of SLG on Ni(111). We found no Rashba splitting at Γ−M confirming ARPES, however, we discovered considerable Rashba splittings in the dispersions along M−K−M, that is, involving the Dirac point, paving the way for SCC by IREE. Thus, for the first time, this work has reconciled the above seemingly contradicting spin-pumping and ARPES experiments, revealed the physical and magnetic origin of SCC by IREE and proposed means to increase the SCC coefficient without the use of heavy precious metals.