Deformation quantization of a Kähler-Poisson structure vanishing on a Levi nondegenerate hypersurface

We give an elementary proof of the result by Leichtnam, Tang, and Weinstein that there exists a deformation quantization with separation of variables on a complex manifold endowed with a Kähler-Poisson structure vanishing on a Levi nondegenerate hypersurface and nondegenerate on its complement.