  Using fully self-consistent N-body models for the dynamical evolution of the
Large Magellanic Cloud (LMC) in the Galaxy, we show that if the LMC initially
has an extended old stellar halo before its commencement of tidal interaction
with the Galaxy, physical properties of the stars stripped from the LMC stellar
halo can have fossil information as to when and where the LMC was accreted onto
the Galaxy for the first time. If the epoch of the first LMC accretion onto the
Galaxy from outside its viriral radius is more than ~4 Gyr ago (i.e., at least
two pericenter passages), the stars stripped from the stellar halo of the LMC
can form an irregular polar ring or a thick disk with a size of ~100 kpc and
rotational kinematics. On the other hand, if the LMC was first accreted onto
the Galaxy quite recently (~ 2 Gyr ago), the stripped stars form shorter
leading and trailing stellar stream at R=50-120 kpc. Also distributions of the
stripped stars in phase space between the two cases can be significantly
different. The derived differences in structure and kinematics of the stripped
stars therefore suggest that if we compare the observed three-dimensional (3D)
distribution and kinematics of the outer Galactic stellar halo along the
polar-axis, then we can give strong constraints on the past orbit of the LMC.
We find that the orbital properties of the LMC in the successful formation
models of the Magellanic Stream (MS) are consistent with those predicted from
recent LambdaCDM cosmological simulations. We conclude that the LMC was
accreted onto the Galaxy more than ~4 Gyr ago so that interaction between the
LMC, the Small Magellanic Cloud (SMC), and the Galaxy could form the MS and its
Leading Arms (LAs).
