The LH2 subunit of Rps. acidophila consists of a ring of 9 αβ heterodimers to which BChl's are associated. We apply the strong exciton coupling model in which all αβ BChl2 pairs are organized in a cyclic unit cell and strongly excitonically coupled. We investigate the exciton energy structure with heterogeneity both in the local BChl850 energies and in transfer integrals. We calculate the pure coherent memory functions of the LH2 subunit which enter the time nonlocal Generalized Master Equations in various regimes of the exciton transfer. We discuss the influence of the exciton interaction with a bath (phonons) on the time dependence of the memory functions and we show limits of the use of the time local Pauli Master Equations. We study also the influence of the heterogeneity in the local BChl850 energies and in transfer integrals on the delivery time of the exciton inside of the LH2.