The double-cover equivalence for quadratic matrix factorizations

Let $G$ be the group acting in the above setup, and let $a_i$ and $x_i$ be the coefficients and coordinates defining the quadratic potential

$$\sum_i a_i x_i^2.$$

Here $\operatorname{MF}$ denotes the category of matrix factorizations. Double-cover equivalence conjecture. There is an equivalence

$$\operatorname{MF}\bigl([\mathbb{A}^n/G]\times\mathbb{A}^n,\;\sum_i a_i x_i^2\bigr)\simeq\operatorname{MF}\bigl([\mathbb{A}^n/\mathbb{Z}_2]\times\mathbb{A}^n,\;\sum_i a_i x_i^2\bigr).$$

The claim identifies the matrix-factorization category for the quotient by $G$ with that for the stacky double cover associated to $\mathbb{Z}_2$. The supplied text gives no evidence that this statement has been proved or disproved.