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In F.-V. Kuhlmann, S. Kuhlmann, M. Marshall, M. Zekavat: "Embedding ordered fields in formal power series fields" we gave a valuation theoretic characterization for a real closed field to be $\kappa$-saturated, for a cardinal $\kappa \geq \aleph_0$. In this paper, we adapt the proof of Theorem 6.2, and generalize the result, giving necessary and sufficient conditions for an o-minimal expansion of a real closed field to be $\kappa$-saturated. ; published