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New experimental data of angular distributions for the 6Li(10B,9Be)7Be reaction were measured at the energy Elab(10B) = 51 MeV for the ground states of nuclei and excited 0.429 - 7.2 MeV states of 7Be. The reaction experimental data were analyzed within coupled-reaction-channels method (CRC) for many types of the nucleon and cluster transfers which spectroscopic amplitudes (factors) in the 9Be and 7Be nuclei were calculated using translation invariant shell model. The Woods - Saxon potential was used for CRC-calculations. The 6Li + 10B potential parameters were deduced before from the analysis of experimental data of 10B ions scattering by 6Li nuclei at the energy Elab(10B) = 51 MeV, and the 9Be + 7Be potential parameters for exit reaction channel were deduced from the CRC calculations fitting to the reaction experimental data. Thus, the information about the 9Be + 7Be optical potential, the basic reaction mechanisms and the 9Be and 7Be nuclei structures were deduced.