Martin's maximum conjecture for forcing extensions of $H_{\aleph_2}$

Let $V$ be a model of ${\text{{\sf MM}}}^{++}$ together with large cardinals, and let $P\in V$ preserve ${\text{{\sf MM}}}^{++}$. Martin's maximum conjecture. For every such $P$,

$$H_{\aleph_2}^V\prec H_{\aleph_2}^{V^P}.$$

This conjecture concerns the invariance of the first-order theory of $H_{\aleph_2}$ under forcing that preserves ${\text{{\sf MM}}}^{++}$. The supplied text does not indicate whether it has been resolved.