The exciton transfer in the light-harvesting complex with the following electron-hole separation in the photosynthetic reaction center dimer is investigated theoretically. The asymmetry in the ring structure of the LH1 antenna complex is assumed. The impact of this asymmetry on exciton transfer is studied. The quantum yields of the electron-hole separation and exciton deactivation into the ground state have been computed. It was shown that the asymmetry does not affect these quantum yields if the coupling between the antenna ring molecules is strong enough. Exciton kinetics are different when asymmetry is present, but the electron-hole separation efficiency is similar to that in the symmetric case. It also showed that the dimer structure in the reaction center is advantageous to the monomeric reaction center structure.