Let R be a commutative ring and $$\mathcal {I}(R)$$ denote the multiplicative group of all invertible fractional ideals of R, ordered by $$A \leqslant B$$ if and only if $$B \subseteq A$$ . We investigate when there is an order homomorphism from $$\mathcal {I}(R)$$ into the cardinal direct sum $$\coprod _{i \in I} G_i$$ , where $$G_i$$ ’s are value groups, if R is a Marot Prufer ring of finite character. Furthermore, over Prufer rings with zero-divisors, we investigate the conditions that make this monomorphism onto.