  We give a new proof of the "super Kazhdan-Lusztig conjecture" for the Lie
super algebra $\mathfrak{gl}_{n|m}(\mathbb{C})$ as formulated originally by the
first author. We also prove for the first time that any integral block of
category O for $\mathfrak{gl}_{n|m}(\mathbb{C})$ (and also all of its parabolic
analogs) possesses a graded version which is Koszul. Our approach depends
crucially on an application of the uniqueness of tensor product
categorifications established recently by the second two authors.
