Let $V_2$ be  the image of $f:V\rightarrow W$; it is  a subsheaf of $W$, hence locally free. Let $W_2$ be the quotient of $W/V_2$ by its torsion subsheaf, and let $W_1$ be the kernel of the projection $W\rightarrow W_2$. The induced map $V_2\rightarrow W_1$ has maximal rank, and you get exactly the situation described in the paper.