The hexagon equation of the non-compact quantum dilogarithm

Let $P$, $Q$, and $V$ be as in Lem.. The hexagon equation of the non-compact quantum dilogarithm.

$$\Phi^{2\hbar}(2P) \Phi^\hbar(Q) = \Phi^\hbar(Q) \Phi^{2\hbar}(2P+2Q) \Phi^\hbar(2P+Q) \Phi^{2\hbar}(2P).$$

This identity is presented as the equation corresponding to Fock–Goncharov's $B_2$-type operator identity. The surrounding discussion gives a heuristic derivation, including a formal limit as $\operatorname{Im}(\hbar)\to 0$, so its status is not established by the supplied text.