Strong self-absorption criterion for coronas

Let $A$ and $D$ be separable and unital $\mathrm{C}^*$-algebras, with $D$ strongly self-absorbing. For a $\mathrm{C}^*$-algebra $B$, write $\mathcal Q(B)=\mathcal M(B)/B$ for its corona algebra, and let $S'$ denote the commutant of $S$. Strong self-absorption criterion for coronas. The following are equivalent:

$$A\otimes D\cong A.$$

For every separable $\mathrm{C}^*$-subalgebra $S$ of $\mathcal Q(A\otimes\mathcal K)$, there is a unital embedding

$$D\hookrightarrow \mathcal Q(A\otimes\mathcal K)\cap S'.$$

This is proposed as an analogue for corona algebras of the corresponding characterization of tensorial absorption. The supplied text gives no resolution, so the conjecture remains open.