Free ordered modules

We establish the necessary and sufficient condition on a partially ordered set $\mathrm{S}$ such that a free ordered $\mathrm{R}$-module ($\mathrm{R}$ is a linearly ordered ring without divisors of zero) over the set $\mathrm{S}$ is $\mathrm{o}$-isomorphic with a free ordered $\mathrm{R}$-module over a trivially ordered set.