We consider the Lie algebra $\mathfrak{g}$ of a simple, simply connectedalgebraic group over a field of large positive characteristic. For eachnilpotent orbit $\mathcal{O} \subseteq \mathfrak{g}$ we choose a representative$e\in \mathcal{O}$ and attach a certain filtered, associative algebra$\widehat{U}(\mathfrak{g},e)$ known as a finite $W$-algebra, defined to be theopposite endomorphism ring of the generalised Gelfand-Graev module associatedto $(\mathfrak{g}, e)$. This is shown to be Morita equivalent to a certaincentral reduction of the enveloping algebra of $U(\mathfrak{g})$. The resultmay be seen as a modular version of Skryabin's equivalence.
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