Separation of variables for the A₃ elliptic Calogero-Moser system

We consider the classical elliptic Calogero-Moser model. A set of canonical separated variables for this model has been constructed in Kuznetsov et al. However, the generating function of the separating canonical transform is known only for two- and three-particle cases. We construct this generating function for the next A₃ case as the limit of the conjectured form of the quantum separating operator. We show explicitly that this generating function gives a canonical transform from the set of original variables to the separated ones.