We prove an equivalence of two $A_{\mathrm{\infty }}$-functors, via Orlov’s Landau–Ginzburg/ Calabi–Yau (LG/CY) correspondence. One is the Polishchuk–Zaslow mirror symmetry functor of elliptic curves, and the other is a localized mirror functor from the Fukaya category of $T^2$ to a category of noncommutative matrix factorizations. As a corollary, we prove that the noncommutative mirror functor $\mathcal{L}{\mathcal{M}}_{gr}^{{\mathbb{L}}_t}$ realizes homological mirror symmetry for any t.