I'd like a detailed proof in English of Laumon's proof that the two Fourier-Mukai transforms taking the derived category of quasicoherent sheaves on $\mathbb{G}_m$-local systems of a curve $X$ to the derived category of $D$-modules on $Bun_{\mathbb{G}_m}(X)$ are mutually inverse.

The original paper is easy to find, but I'd ideally like an English translation, or at least an expository paper in English.