Squashed entanglement [Christandl and Winter, J. Math. Phys. 45(3):829-840 (2004)] is a monogamous entanglement measure, which implies that highly extendible states have small value of the squashed entanglement. Here, invoking a recent inequality for the quantum conditional mutual information [Fawzi and Renner, Commun. Math. Phys. 340(2):575-611 (2015)] greatly extended and simplified in various work since, we show the converse, that a small value of squashed entanglement implies that the state is close to a highly extendible state. As a corollary, we establish an alternative proof of the faithfulness of squashed entanglement [Brandão, Christandl and Yard, Commun. Math. Phys. 306:805-830 (2011)].We briefly discuss the previous and subsequent history of the Fawzi-Renner bound and related conjectures, and close by advertising a potentially farreaching generalization to universal and functorial recovery maps for the monotonicity of the relative entropy.Squashed entanglement.-One of the core goals in the theory of entanglement is its quantification, for which purpose a large number of either operationally or mathematically/axiomatically motivated entanglement measures and monotones have been introduced and studied intensely since the 1990s [20,9].In this paper we will discuss one specific such measure, the so-called squashed entanglement [12], defined as E sq (ρ AB ) := inf 1 2 I(A : B|E) s