As a consequence of the Littlewood-Richardson (LR) commuters coincidence and the Kumar-Torres branching model via Kushwaha-Raghavan-Viswanath flagged hives, one has solved the Lecouvey-Lenart conjecture on the  bijections between the Kwon and Sundaram branching models for the pair consisting of the general linear group \( {GL}_{2n}(\mathbb{C}) \) and the symplectic group \( {Sp}_{2n}(\mathbb{C}) \). In particular, thanks to the Henriques-Kamnitzer \( gl_n \)-crystal commuter,  one has recognized that the left companion of an LR-Sundaram tableau is characterized by the Kwon symplectic property. One now shows that the construction of the left companion tableau mirrors, in fact, the Sundaram property as the Kwon symplectic property.