Let $\Lambda\subset T^{\ast}_{B}$ and $\Lambda^{\prime}\subset T^{\ast}_{B^{\prime}}$ be the lattices induced from the integral affine structures on $B$ and $B^{\prime}$, respectively. From Theorem 3.3 it follows that $X$ and $X^{\prime}$ are symplectomorphic to $T^{\ast}_{B}/\Lambda$ and $T^{\ast}_{B^{\prime}}/\Lambda^{\prime}$, respectively. Given an integral affine isomorphism $\phi$ between $B$ and $B^{\prime}$, clearly $\phi^{\ast}$ is a symplectomorphism between $T^{\ast}_{B^{\prime}}$ and $T^{\ast}_{B}$ inducing an isomorphism between $\Lambda^{\prime}$ and $\Lambda$. Therefore $\phi^{\ast}$ descends to a symplectomorphism $\tilde{\psi}$ between $T^{\ast}_{B^{\prime}}/\Lambda^{\prime}$ and $T^{\ast}_{B}/\Lambda$. Defining $\psi=\Theta^{\prime}\circ(\tilde{\psi})^{-1}\circ\Theta^{-1}$ the claim follows. ∎