With the hypothesis of Proposition 4.72, let $\psi_{2}$ be an H-lattice concave function on $\Pi_{2}$ and let $D_{\psi_{2}}$ be the corresponding semipositive $\mathbb{T}$-Cartier divisor. Then $\Phi_{p,A}^{\ast}D_{\psi_{2}}$ is the semipositive $\mathbb{T}$-Cartier divisor associated to the H-lattice concave function $\psi_{1}=A^{\ast}\psi_{2}$. Moreover the Legendre-Fenchel dual is given by