  We simulate the first minutes of the evolution of a binary-driven hypernova
(BdHN) event, with a special focus on the associated accretion processes of
supernova (SN) ejecta onto the newborn neutron star ($\nu$NS) and the NS
companion. We calculate the rotational evolution of the $\nu$NS and the NS
under the torques exerted by the accreted matter and the magnetic field. We
take into account general relativistic effects and use realistic hypercritical
accretion rates obtained from three-dimensional smoothed-particle-hydrodynamics
(SPH) numerical simulations of the BdHN for a variety of orbital periods. We
show that the rotation power of the $\nu$NS has a unique double-peak structure
while that of the NS has a single peak. These peaks are of comparable intensity
and can occur very close in time or even simultaneously depending on the
orbital period and the initial angular momentum of the stars. We outline the
consequences of the above features in the early emission and their consequent
observation in long gamma-ray bursts (GRBs).
