I’ve just proved the following:

Theorem $(\mathsf{FCD}) (\mathsf{RLD})_{\Gamma} f = f$ for every funcoid $f$.

For a proof see this online article.

I’ve also posed the conjecture:

Conjecture $(\mathsf{FCD}) : \mathsf{RLD} (A ; B) \rightarrow \mathsf{FCD} (A ; B)$ is the upper adjoint of $(\mathsf{RLD})_{\Gamma} : \mathsf{FCD} (A ; B) \rightarrow \mathsf{RLD} (A ; B)$ for every sets $A$, $B$.

I have also proved that $(\mathsf{RLD})_{\Gamma}$ is neither upper nor lower adjoint of $(\mathsf{FCD})$ (see the same online article above).