GHH Preferences: FOC
The first-order condition would be satisfied under the assumption $c=G(l)$ if $U'(0)=0$. But this latter requirement is incompatible with the assumptions: indeed, $U'$ is nonincreasing (by the concavity of $U$) which yields $U'(x) \leq 0$ for any $x \geq 0$, which contradicts the fact that $U$ is increasing. 

If $U'(x)&gt;0$ for all $x$, the only possibility to meet the first-order condition is indeed $\dfrac{dc}{dl}=G'(l)$.