Geometrical-phase lens based optical system for the spin-splitting of vector beams

•We combine a geometric phase lens and a telescope to produce an optical system with two polarization controlled real foci with equal magnification.•We apply it to characterize vortex beams and vector beams, splitting longitudinally the circular polarization components and focusing them into different axial planes.•We show the polarization interference pattern obtained at an intermediate plane, which easily reveals the difference and relative sign of the vector beam's topological charge at each circular component.•This interference pattern can be used to identify the vector beam of a given order through the relative phase between the RCP and LCP components, which is clearly visible in the shift of the interference pattern at the intermediate plane.