Continuity conjecture for synthetic curvature measures

Let $X_i\in\text{Alex}^n(-1)$ be a sequence of Alexandrov spaces converging to $X$ in the Gromov–Hausdorff sense without collapsing. Let $\mu_{X_i}$ and $\mu_X$ denote their synthetic curvature measures. Continuity conjecture. Then

$$\mu_{X_i}\to\mu_X.$$

This proposes continuity of the synthetic curvature measure under non-collapsing Gromov–Hausdorff convergence. The source presents it as an open question and gives no resolution.