________for many years,nobody could recognize him.

两个都是独立主格结构，但二者表示的时间概念不同：

The man being put in prison, 表示被put in prison 的时间与recognize 同时发生， 即：由于正被关在监牢里，这时候没人能够认出他来；

The man having been put in prison? 表示被put in prison 的时间早于recognize，即：由于早在以前被关在监狱里过，过后没人能够认出他来。

后者从逻辑上不合情理上

我觉得应该用having been put in prison ,
Having been put in prison for many years, nobody could recognize him.

都不对，应该是The man has been put into prison for many years and nobody can recognize him