I vaguely remember_something like that.A.him having said B.his saying 为什么?

B
这是动名词的复合结构的用法.
动名词的复合结构即“逻辑主语 + 动名词”结构.动名词的逻辑主语由物主代词或名词所有格充当.如 David’s opening the window made us angry./ His coming late has some reasons.