Summary: Due to an example indicated to us in September 2009, we have to add one more restriction to the suppositions on the imprimitivity bimodules treated in Proposition 4.1, Theorem 5.1, Theorem 6.2 and Proposition 6.3 of [ibid. 3, No. 2, 91--102 (2009; Zbl 1206.46009
)]. In the situation when the Banach-Saks property holds for the imprimitivity bimodule, we can describe all possible additional examples violating the newly invented supposition, so the classification of Hilbert $C^*$-modules with the Banach-Saks property is complete. Beyond that, there is still an open problem for a certain class of imprimitivity bimodules with the weak or uniform weak Banach-Saks property which might violate the additional condition.