  In this paper, we classify simple strong Harish-Chandra modules over the Lie
superalgebra $W_{m,n}$ of vector fields on $\C^{m|n}$. Any such module is the
unique simple submodule of some tensor module $F(P,V)$ for a simple weight
module $P$ over the Weyl superalgebra $\mathcal K_{m,n}$ and a simple weight
module $V$ over the general linear superalgebra $\gl_{m,n}$.
