We have investigated the electron spin dynamics on the discrete energy levels of self-organized InAs quantum dots (QDs) covered by the thin InGaAs layer and embedded in the GaAs matrix. The InGaAs layer forms the external quantum well (QW). In particular, we report on the electron mean spin redistribution over the QD and QW energy spectrum resulting in a drastic increase of electron spin polarization of the QD excited levels and the QW ground state. The electron polarization is determined by measuring the degree of circular polarization of the QD and QW emissions after excitation by 1.5 ps circular polarized pulses in the GaAs barrier.