  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 GaiaEDR3, 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.
