  In studying the structure of derived categories of module categories of group
algebras or their blocks, it is fundamental to classify support $\tau$-tilting
modules. Koshio and Kozakai showed that the structure of support $\tau$-tilting
modules over blocks of finite groups can be reduced to that of their subgroups
under suitable conditions. We show that the 'quotient reduction' is also valid
under suitable conditions.
