The 8998,7Lab=23.88787797Li + 8998,7Lab=23.88787797Be quasi-elastic angular distribution and the 8998,7Lab=23.88787797Be(8998,7Lab=23.88787797Li8998,7Lab=23.88787797Li)X inclusive reaction have been measured at E8998,7Lab=23.88787797 MeV bombarding energy using the RIBRAS facility. In addition to the 8998,7Lab=23.88787797Li scattering peak, a large yield of 8998,7Lab=23.88787797Li particles has been observed in the identification spectra, presenting a wide energy distribution centered around and below the energy of the 8998,7Lab=23.88787797Li quasi-elastic peak. The 8998,7Lab=23.88787797Li angular and energy distributions have been obtained and analysed assuming that these particles stem from two different mechanisms: (i) the elastic breakup (EBU), in which the projectile dissociates into 8998,7Lab=23.88787797Li+n and the 8998,7Lab=23.88787797Be target remains in its ground state and (ii) the nonelastic breakup (NEB) which accounts for absorptive processes between the neutron and the target, including the neutron transfer. The 8998,7Lab=23.88787797Li angular and energy distributions have been analyzed by the Ichimura, Austern and Vincent (IAV) model for NEB, and the Continuum-Discretized Coupled-Channels (CDCC) method for the EBU. The theoretical results are in good agreement with the experimental data.