  The Lax pair for the field analogue of the classical spin elliptic
Calogero-Moser is proposed. Namely, using the previously known Lax matrix we
suggest an ansatz for the accompany matrix. The presented construction is valid
when the matrix of spin variables ${\mathcal S}\in{\rm Mat}(N,\mathbb C)$
satisfies the condition ${\mathcal S}^2=c_0{\mathcal S}$ with some constant
$c_0\in\mathbb C$. It is proved that the Lax pair satisfies the Zakharov-Shabat
equation with unwanted term, thus providing equations of motion on the
unreduced phase space. The unwanted term vanishes after additional reduction.
In the special case ${\rm rank}(\mathcal S)=1$ we show that the reduction
provides the Lax pair of the spinless field Calogero-Moser model obtained
earlier by Akhmetshin, Krichever and Volvovski.
