For any $\beta\in\Gamma_{c}(P(L_{1},L_{2}),\underline{Hom}^{alg}(E_{1},E_{2}))$ there exists a limit in the sense of distributions

$$\psi^{\infty}(\beta)=lim_{t\to+\infty}\psi^{t}(\beta)\in\Gamma(P(L_{1},L_{2}),{{\bf C}}_{\varepsilon}^{tw}\otimes(\widehat{\rho}_{1}^{\ast}\otimes\widehat{\rho}_{2})\otimes\underline{D}_{P(L_{1},L_{2})}^{\prime})\,,$$

where $\underline{D}_{P(L_{1},L_{2})}^{\prime}$ is the sheaf of distribution-valued differential forms on $P(L_{1},L_{2})$.