Let $(L,z)$ be a toric line bundle on $X_{\Sigma}$ and $\sigma\in\Sigma$. Let $\Psi$ be a virtual support function such that $\Psi|_{\sigma}=0$ and $(L,z)\simeq(L_{\Psi},z_{\Psi})$ as toric line bundles. Then $\iota^{\ast}_{\sigma}(L,z)\simeq(L_{\Psi(\sigma)},z_{\Psi(\sigma)})$.