  Let $e$ be an arbitrary even nilpotent element in the general linear Lie
superalgebra $\mathfrak{gl}_{M|N}$ and let $\mathcal{W}_e$ be the associated
finite $W$-superalgebra. Let $Y_{m|n}$ be the super Yangian associated to the
Lie superalgebra $\mathfrak{gl}_{m|n}$. A subalgebra of $Y_{m|n}$, called the
shifted super Yangian and denoted by $Y_{m|n}(\sigma)$, is defined and studied.
Moreover, an explicit isomorphism between $\mathcal{W}_e$ and a quotient of
$Y_{m|n}(\sigma)$ is established.
