Let $V$ be a vertex operator algebra, $T\in \N$ and $(M^k, Y_{M^k})$ for $k=1, 2, 3$ be a $g_k$-twisted module, where $g_k$ are commuting automorphisms of $V$ such that $g_k^T=1$ for $k=1, 2, 3$ and $g_3=g_1g_2$. Suppose $I(\cdot, z)$ is an intertwining operator of type $\left(\begin{array}{c}M^{3} \ M^{1} M^{2} \end{array}\right) $. We construct an $A_{g_1g_2}(V)$-$A_{g_2}(V)$-bimodule $A_{g_1g_2, g_2}(M^1)$ which determines the action of $M^1$ from the bottom level of $M^2$ to the bottom level of $M^3$.