Factorizing a linear map through another one that has a smaller kernel

Question

Let $E,F,G$ be 3 vectors spaces and $U \in L(E,F)$, $W \in L(E,G)$.

Show that if $\ker(U)$ is included in $\ker(W)$ then there is a linear map $V \in L(F,G)$ such that $W=U\circ V$.

If $U$ is bijective then it's simple to write $V=W\circ U^{-1}$. But how can I find $V$ if $U$ is not bijective ?