  We establish a correspondence between rational solutions to the matrix KP
hierarchy and the spin generalization of the Calogero-Moser system on the level
of hierarchies. Namely, it is shown that the rational solutions to the matrix
KP hierarchy appear to be isomorphic to the spin Calogero-Moser system in a
sense that the dynamics of poles of solutions to the matrix KP hierarchy in the
higher times is governed by the higher Hamiltonians of the spin Calogero-Moser
integrable hierarchy with rational potential.
