Several commentaries ask the question on Esther 2:5 as to why the passuk says Ben Kish when Shim'i was Kish's fifth-great grandson (Targum Sheini). Some explain it's because Mordechai shared traits of Kish's (Yalkut 1053). Others say it's because Kish was Shim'i's maternal grandfather and therefore could be called his son (Maharsha Megillah 13b).
The Megillas Sesarim explains that he's called ben Shim'i because it was in Mordechai's zechus that Shim'i wasn't killed, and he is called ben Kish because Mordechai rectified the sin of Sha'ul, which resulted in Haman's birth. According to this explanation, why is Mordechai called ben Kish and not ben Sha'ul, Kish's son?