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Then $M^{\\otimes s}$ is a $(S(n,rs), F\\mathfrak{S}_s)$-bimodule, where the symmetric group $\\mathfrak{S}_s$ on $s$ letters acts on the right by place permutations. We show that the Schur functor $f_{rs}$ sends $M^{\\otimes s}$ to the $(F\\mathfrak{S}_{rs},F\\mathfrak{S}_s)$-bimodule $F\\mathfrak{S}_{rs} \\otimes_{F(\\mathfrak{S}_r \\wr \\mathfrak{S}_s)} ((f_rM)^{\\otimes s} \\otimes F\\mathfrak{S}_s)$. 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