Two new open problems about relationships of funcoids and reloids

In the past I overlooked the following two open problems considering them obvious. When I tried to write proofs of these statements down I noticed these are not trivial. So I added them to my list of open problems.

Question $latex (\mathsf{RLD})_{\mathrm{out}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B}) = \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B}$ for every filter objects $latex \mathcal{A}$, $latex \mathcal{B}$?

Conjecture $latex (\mathsf{RLD})_{\mathrm{out}} {(=)}|_{\mathcal{A}} = {(=)}|_{\mathcal{A}}$ for every filter object $latex \mathcal{A}$.