Lemma 58.19.7. In Situation 58.19.1 assume $A$ has depth $\geq 3$ and $A$ is henselian or more generally $(A, (f))$ is a henselian pair. Then the restriction functor $\textit{FÉt}_ U \to \textit{FÉt}_{U_0}$ is fully faithful.

**Proof.**
The assumption of depth forces $H^1_\mathfrak m(A) = H^2_\mathfrak m(A) = 0$, see Dualizing Complexes, Lemma 47.11.1. Hence Lemma 58.19.6 applies.
$\square$

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