I’ve added to the preprint of my book a new theorem (currently numbered theorem 8.30).
The theorem states:
Theorem $latex g \circ ( \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B}) \circ f =
\langle ( \mathsf{FCD}) f^{- 1} \rangle \mathcal{A}
\times^{\mathsf{RLD}} \langle ( \mathsf{FCD}) g \rangle
\mathcal{B}$ for every reloids $latex f$, $latex g$ and filters $latex \mathcal{A} \in
\mathfrak{F}^{\mathrm{Dst}\, f}$, $latex \mathcal{B} \in \mathfrak{F}^{\mathrm{Src}\, g}$.