Global sections of sheafification of Cohen-Macaulay module

Question

Let $S=k[x_0,\ldots,x_n]$ be the polynomial ring over a field $k$ with the standard grading. Let $M$ be a finitely generated graded Cohen-Macaulay $S$-module of dimension at least two. Let $\mathcal{F}=\tilde{M}$ be the corresponding sheaf on $\mathbb{P}^n$. Then we have that $\sum_{j \in \mathbb{Z}} H^0(\mathbb{P}^n, \mathcal{F}(j)) \cong M$. I know how to proof that using local cohomology and Ext-groups, but I think it is a pretty standard fact that should be phrased somewhere citably. Does anyone know a good reference to cite that?