Hellus's associated-prime conjecture for Matlis duals of local cohomology

Let $(R,\mathfrak{m})$ be a Noetherian regular local ring, let $I$ be a non-zero ideal of $R$, and let $E:=E_R(R/\mathfrak{m})$ be an injective hull of the residue field. For any $R$-module $M$, write $D(M):=\operatorname{Hom}_R(M,E)$, and write $\operatorname{H}^i_I(R)$ for the $i$-th local cohomology module supported in $I$.

Hellus's conjecture. If $\operatorname{H}^i_I(R)\neq 0$, then

$$0\in \operatorname{Ass}_R\bigl(D(\operatorname{H}^i_I(R))\bigr).$$

This extends Hellus's equivalent domain condition from ideals generated by a specified number of elements to arbitrary non-zero ideals in regular local rings. The supplied text says that the corresponding associated-prime conjecture is known in many cases, but gives no resolution of this proposed generalization.