  The Local Group is often seen to be a quiescent environment without
significant merger events. However an ancient major merger may have occurred in
the most massive galaxy. Numerical simulations have shown that tidal tails
formed during gas-rich major mergers are long-lived and could be responsible
for old stellar streams and likely induce the formation of tidal dwarf galaxies
(TDGs). Using several hydrodynamical simulations we have investigated the most
prominent tidal tail formed during the first passage, which is gas-rich and
contains old and metal poor stars. We discovered several striking coincidences
after comparing its location and motion to those of the Milky Way (MW) and of
the Magellanic Clouds (MCs). First, the tidal tail is sweeping a relatively
small volume in which the MW precisely lies. Because the geometry of the merger
is somehow fixed by the anisotropic properties of the Giant Stream (GS), we
evaluate the chance of the MW to be at such a rendez-vous with this gigantic
tidal tail to be 5 %. Second, the velocity of the tidal tail matches the LMC
proper motion, and reproduce quite well the geometrical and angular momentum
properties of the MW dwarfs, i.e. the so-called disk of satellites, better
called Vast Polar Structure (VPOS). Third, the simulation of the tidal tail
reveals one of the formed TDG with mass and location almost comparable to those
of the LMC. Our present modeling is however too limited to study the detailed
interaction of gas-rich TDGs with the potential of the MW, and a complementary
study is required to test whether the dwarf intrinsic properties can be
accounted for by our scenario. Nevertheless this study suggests a causal link
between an ancient, gas-rich major merger at the M31 location, and several
enigma in the Local Group, the GS, the VPOS, and the presence of the MCs.
