Let $S$ be a graded noetherian ring and $M$ a finitely generated graded $S$- module. Then I know that there exists a filtration
$0=M_0 \subseteq M_1\subseteq \cdots \subseteq M_r=M$ by graded submodules such that for each $i$, $M_i/M_{i-1}=(S/P_i)(l_i)$ for some homogeneous prime ideal $P_i$ of $S$ and $l_i$ integer, where $(S/P_i)(l_i)$ shift module.
I wonder if $M$ can be expressed in the form $(S/P)(l)$ for some homogeneous prime ideal of $S$. Is it possible?