  There is a population of stars with velocities in excess of 500 km s$^{-1}$
relative to the Galactic center. Many, perhaps most, of these hyper-velocity
stars (HVSs) are B stars, similar to the disk and S stars in a nuclear cluster
around a super-massive black hole (SMBH) near $\rm Sgr~A^{\star}$. In the paper
I of this series, we showed that the eccentricity of the stars emerged from a
hypothetical disk around the SMBH can be rapidly excited by the secular
perturbation of its intermediate-mass companion (IMC), and we suggested IRS 13E
as a potential candidate for the IMC. Here, we show that this process leads to
an influx of stars on parabolic orbits to the proximity of $\rm Sgr~A^{\star}$
on a secular timescale of a few Myr. This timescale is much shorter than the
diffusion timescale into the lost cone through either the classical or the
resonant relaxation. Precession of the highly-eccentric stars' longitude of
periastron, relative to that of the IMC, brings them to its proximity within a
few Myr. The IMC's gravitational perturbation scatters a fraction of the stars
from nearly parabolic to hyperbolic orbits, with respect to the SMBH. Their
follow-up close encounters with the SMBH induce them to escape with
hyper-velocity. This scenario is a variant of the hypothesis proposed by Hills
based on the anticipated breakup of some progenitor binary stars in the
proximity of the SMBH, and its main objective is to account for the limited
lifespan of the known HVSs. We generalize our previous numerical simulations of
this process with a much wider range of orbital configurations. We demonstrate
the robustness and evaluate the efficiency of this channel of HVS formation.
From these numerical simulations, we infer observable kinematic properties for
the HVSs.
