  It has been recently shown that the halo near the Sun contains several
kinematic substructures associated to past accretion events. For the more
distant halo, there is evidence of large-scale density variations -- in the
form of stellar clouds or overdensities. We study the link between the local
halo kinematic groups and three of these stellar clouds: the Hercules-Aquila
cloud, the Virgo Overdensity, and the Eridanus-Phoenix overdensity. We perform
orbital integrations in a standard Milky Way potential of a local halo sample
extracted from Gaia eDR3, with the goal of predicting the location of the
merger debris elsewhere in the Galaxy. We specifically focus on the regions
occupied by the three stellar clouds and compare their kinematic and distance
distributions with those predicted from the orbits of the nearby debris. We
find that the local halo substructures have families of orbits that tend to
pile up in the regions where the stellar clouds have been found. The distances
and velocities of the cloud's member stars are in good agreement with those
predicted from the orbit integrations, particularly for Gaia-Enceladus stars.
This is the dominant contributor of all three overdensities, with a minor part
stemming from the Helmi streams and to an even smaller extent from Sequoia. The
orbital integrations predict no asymmetries in the sky distribution of halo
stars, and they pinpoint where additional debris associated with the local halo
substructures may be located.
