Integrability of the multi-species TASEP with species-dependent rates

Assume that each species $l$ has its own jump rate $b_l$ in the multi-species totally asymmetric simple exclusion process. We show that this model is \textit{integrable} in the sense that the Bethe Ansatz method is applicable to obtain the transition probabilities for all possible $N$-particle systems with up to $N$ different species.