When $G\subset E_{\overline{K}}$ is invariant by $\operatorname{Gal}(\overline{K}/K)$, can we construct $K$-isogeny s.t. the kernel is $G$?

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Sorry for my bad English.

In AEC Remark 4.13.2, there is the following proposition

Let $K$ be a field, $E$ be an elliptic curve over $K$, and $G\subset E(\overline{K})$ be a finite subgroup. If $G$ is invariant by the action of $\operatorname{Gal}(\overline{K}/K)$, there is unique isogeny $\phi: E\to E'$ over $K$ s.t. $\operatorname{Ker}(\phi)=G$.

In the above, we denote $\operatorname{Ker}(\phi)$ as a kernel of $\phi_{\overline{K}}: E_{\overline{K}}\to E'_{\overline{K}}$.

Now I want to know that if we can generalize $G\subset E(\overline{K})$ for a finite subgroup scheme $G\subset E_{\overline{K}}$.

I can understand a basic algebraic geometry, scheme theory, finite group scheme theory.

Please tell me this theory, books, or articles.