Enhancement uniqueness conjecture for complicial Grothendieck prestable categories

Let $\mathcal{A}$ be an $n$-complicial separated Grothendieck prestable $\infty$-category, and let $\mathcal{C}$ be a stable presentable $\infty$-category. Suppose there is an exact equivalence

$$h_{n-1}\mathcal{C}\simeq h_{n-1}\mathcal{S}\mathrm{p}(\mathcal{A})$$

of stable $n$-categories.

Enhancement uniqueness conjecture. Then

$$\mathcal{C}\simeq\mathcal{S}\mathrm{p}(\mathcal{A}).$$

The $n=0$ case is identified with a theorem earlier in the paper. The proposed proof depends on a not-yet-rigorous notion of exact functor between stable $n$-categories, so the general statement remains open.