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Suppose $M^1$ is a $g_1$-twisted module. For any $n, m\\in \\frac{1}{T}\\N$, we construct an $A_{g_3, n}(V)$-$A_{g_2, m}(V)$-bimodule $\\mathcal{A}_{g_3, g_2, n, m}(M^1)$ associated to the quadruple $(M^1, g_1, g_2, g_3)$. Given an $A_{g_2, m}(V)$-module $U$, an admissible $g_3$-twisted module $\\mathcal{M}(M^1, U)$ is constructed. 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