  This is the second paper in a series, which studies the likelihood that some
globular clusters (GCs) of the Milky Way (MW) could have originated from a
dwarf satellite galaxy (DSG). Using a large suite of three-body simulations we
determine the present-day orbital properties of 154 GCs that could have escaped
from 41 MW DSGs over the past $8\,\mathrm{Gyrs}$. For the MW we considered two
sets of static and dynamic models which account for the sustained growth of the
MW since its birth. We focus on the Magellanic Clouds and Sagittarius. We
compare the apogalactic distance, eccentricity, and orbital inclination of the
MW GCs with those of runaway GCs from DSGs, to constrain their possible ex-situ
origin. We observe a positive correlation between a DSG mass and the dispersion
of its runaway GCs in the orbital parameter space of ($R_\mathrm{ap}$, $e$). We
provide tables of the identified MW GCs and their likely associated
progenitors. In total, we find 29 (19%) MW GCs which could be kinematically
associated with MW DSGs. We report, for the first time, 6 and 10 new
associations with the Large Magellanic Cloud and the Sagittarius, respectively.
For the Sagittarius we predict a concentration of runaway GCs at large
apogalactic distances of $R_\mathrm{ap}\approx275-375\,\mathrm{kpc}$,
$e\approx0.8$, and a relative inclination of $\Delta\theta\approx20^{\circ}$.
So far, there has not been any observed GCs with such orbital elements.
Complemented with photometric and spectroscopic observations, and cosmological
simulations, the findings from the present study could conclusively settle the
debate over the in-situ vs. ex-situ origin of the MW GCs.
