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We consider solutions of the matrix KP hierarchy that are elliptic functionsof the first hierarchical time $t_1=x$. It is known that poles $x_i$ and matrixresidues at the poles $\rho_i^{\alpha \beta}=a_i^{\alpha}b_i^{\beta}$ of suchsolutions as functions of the time $t_2$ move as particles of spingeneralization of the elliptic Calogero-Moser model (elliptic Gibbons-Hermsenmodel). In this paper we establish the correspondence with the spin ellipticCalogero-Moser model for the whole matrix KP hierarchy. Namely, we show thatthe dynamics of poles and matrix residues of the solutions with respect to the$k$-th hierarchical time of the matrix KP hierarchy is Hamiltonian with theHamiltonian $H_k$ obtained via an expansion of the spectral curve near themarked points. The Hamiltonians are identified with the Hamiltonians of theelliptic spin Calogero-Moser system with coordinates $x_i$ and spin degrees offreedom $a_i^{\alpha}, \, b_i^{\beta}$.

Elliptic solutions to matrix KP hierarchy and spin generalization of elliptic Calogero-Moser model