The lifting conjecture for the Huneke–Wiegand property

Let $(R,\mathfrak m)$ be a Gorenstein local ring and let $x\in\mathfrak m$ be a non-zerodivisor. Say that $R$ satisfies (HW) when every torsion-free $R$-module $M$ with rank such that $M\otimes_R M^*$ is maximal Cohen–Macaulay is free, where $M^*=\operatorname{Hom}_R(M,R)$.

Huneke–Wiegand lifting conjecture. If $R/(x)$ satisfies (HW), then $R$ satisfies (HW).

This asks whether the Huneke–Wiegand property lifts across a quotient by a regular element. The supplied text gives no resolution, so the conjecture remains open.