  It is found that the Hamiltonian of S=1/2 isotropic Heisenberg chain with $N$
sites and elliptic non-nearest-neighbor exchange is diagonalized in each sector
of the Hilbert space with magnetization $N/2-M$, $1<M\leq[N/2]$, by means of
double quasiperiodic meromorphic solutions to the $M$-particle quantum
Calogero-Moser problem on a line. The spectrum and highest-weight states are
determined by the solutions of the systems of transcendental equations of the
Bethe-ansatz type which arise as restrictions to particle pseudomomenta.
