Her often being late makes me angry.可以说成 Her being often late makes me angry.为什么呢

不可以
“Her often being late ”作的是这句话的主语,“being late”在此处的作用是名词（动名词短语）,应该是个整体,而often是用来修饰的,与She is often late中 often是副词修饰形容词late的.
不知道这么说有没有让你理解点.she is often late中的often是放在复合谓语之间的，那么Her being often late 不也是的吗