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We give a precise non trivial counterexample to the existence of the Møller morphism for groups of *-automorphism describing a two-body interacting dynamical system. This fact invalidate the property of L1 asymptotic abelianness which is a crucial ingredient in many developments of the non-stationary approach on the stability of KMS states. It is build on the spin fermion dynamical system, nevertheless it is typically what we should expect when we consider a generic case of a small system interacting with a reservoir.