  We provide an expression for the conductor $c(\Delta)$ of a semimodule
$\Delta$ of a numerical semigroup $\Gamma$ with two generators in terms of the
syzygy module of $\Delta$ and the generators of the semigroup. In particular,
we deduce that the difference between the conductor of the semimodule and the
conductor of the semigroup is an element of $\Gamma$, as well as a formula for
$c(\Delta)$ in terms of the dual semimodule of $\Delta$.
