Finite-dimensional vertex algebra modules over fixed point differential subfields

Let $K$ be a differential field over $\C$ with derivation $D$, $G$ a finite linear automorphism group over $K$ which preserves $D$, and $K^G$ the fixed point subfield of $K$ under the action of $G$. We show that every finite-dimensional vertex algebra $K^G$-module is contained in some twisted vertex algebra $K$-module.