  We construct an algebra morphism from the elliptic quantum group
$E_{\tau,\eta}(sl_2)$ to a certain elliptic version of the ``quantum groups in
higher genus'' studied by V. Rubtsov and the first author. This provides an
embedding of $E_{\tau,\eta}(sl_2)$ in an algebra ``with central extension''. In
particular we construct $L^{\pm}$-operators obeying a dynamical version of the
Reshetikhin--Semenov-Tian-Shansky relations. To do that, we construct the
factorization of a certain twist of the latter algebra, that automatically
satisfies the ``twisted cocycle condition'' of O. Babelon, D. Bernard and E.
Billey, and therefore provides a solution of the dynamical Yang-Baxter
equation.
