  We investigate when an ordered abelian group $G$ is stably embedded in a
given elementary extension $H$. We focus on a large class of ordered groups
which includes maximal ordered groups with interpretable archimedean valuation.
We give a complete answer for groups in this class which takes the form of a
transfer principle for valued groups. It follows in particular that all types
in the lexicographic product $\prod_{i\in \omega} \mathbb{Z}$ are definable.
