  As a sequel to [CS13b], we verify the so-called inductive AM-condition
introduced in [Sp12] for simple groups of type A and blocks with maximal
defect. This is part of the program set up to verify the Alperin-McKay
conjecture through its reduction to a problem on quasi-simple groups (see
[Sp13]) but also the missing direction of Brauer's height zero conjecture (see
[NS14])
