Kac-Moody algebras and their variations play a crucial role in various parts of mathematics and physics. For instance, in the framework of the study of K-theoretical Coulomb branches, Finkelberg-Tsymbaliuk introduced recently remarkable new algebras, the shifted quantum affine Kac-Moody algebras and their truncations. We propose a conjectural parameterization of simple representations of a non simply-laced truncation in terms of the Langlands dual quantum affine Kac-Moody Lie algebra. We establish the statement for finite-dimensional representations, using the existence of Baxter polynomials for the corresponding quantum integrable systems.