Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring

We show that two blocks of generalized quaternion defect with three simple modules over a sufficiently large 2-adic ring OO are Morita-equivalent if and only if the corresponding blocks over the residue field of OO are Morita-equivalent. As a corollary we show that any two blocks defined over OO with three simple modules and the same generalized quaternion defect group are derived equivalent.