  Nonequilibrium dynamics of the open chain Holstein-Hubbard model is studied
using the linear time-scaling GKBA+ODE scheme developed in the preceeding
paper. We focus on the set of parameters relevant for photovoltaic materials,
i.\,e., a pair of electrons interacting with phonons at the cross-over between
the adiabatic and anti-adiabatic regimes and at moderately large
electron-electron interaction. By comparing with exact solutions for two corner
cases, we demonstrate the accuracy of the $T$-matrix (in the $pp$ channel) and
the second-order Fan ($GD$) approximations for the treatment of electronic
($e$-$e$) and electron-phonon ($e$-ph) correlations, respectively. The feedback
of electron on phonons is consistently included and is shown to be mandatory
for the total energy conservation. When two interactions are simultaneously
present, our simulations offer a glimpse into the dynamics of doublons and
polarons unveiling the formation, propagation and decay of these
quasiparticles, energy redistribution between them and self-trapping of
electrons.
