Summary: We tackle the still open problem of the decidability of the existence of a coding \(F\) between two trace monoids \(M_1\), \(M_2\), when \(M_1\) is a free product of free commutative monoids. We propose that a coding morphism always exists between \(M_1\) and \(M_2\) for particular trace monoids \(M_2\).