Type A blocks of super category O

We show that every block of category O for the general linear Lie superalgebra glm|n(k) is equivalent to some corresponding block of category O for the queer Lie superalgebra qm+n(k). This implies the truth of the Kazhdan-Lusztig conjecture for the so-called type A blocks of category O for the queer Lie superalgebra as formulated by Cheng, Kwon and Wang.