We show here theoretically and experimentally that a Rashba-split electron state inside a ferromagnet can efficiently convert a dynamical spin accumulation into an electrical voltage. The effect is understood to stem from the Rashba splitting but with a symmetry linked to the magnetization direction. It is experimentally measured by spin pumping in a CoFeB/MgO structure where it is found to be as efficient as the inverse spin Hall effect at play when Pt replaces MgO, with the extra advantage of not affecting the damping in the ferromagnet.