It's would have made a great movie/film plot if we could say that Esther was a lineal descendant of King Saul, but based on the following bible genealogy, it does Not seem that way. However, in both King Saul's genealogy and Esther's genealogy, it mentions the individual named Kish who was King Saul's father. Would it be correct to say that Esther was a "closely related" collateral descendant of King Saul?
(1 Samuel 9:1-2)
Now there was a man of Benjamin whose name was Kish the son of Abiel, the son of Zeror, the son of Becorath, the son of Aphiah, the son of a Benjamite, a mighty man of valor. 2 He had a son whose name was Saul,........
(1 Samuel 14:50-51)
The name of Saul’s wife was Ahinoam the daughter of Ahimaaz. And the name of the captain of his army was Abner the son of Ner, Saul’s uncle. 51 Kish was the father of Saul, and Ner the father of Abner was the son of Abiel.
5 Now there was at the citadel in Susa a Jew whose name was Mordecai, the son of Jair, the son of Shimei, the son of Kish, a Benjamite, 6 who had been taken into exile from Jerusalem with the captives who had been exiled with Jeconiah king of Judah, whom Nebuchadnezzar the king of Babylon had exiled. 7 He was bringing up Hadassah, that is Esther, his uncle’s daughter, for she had no father or mother. Now the young lady was beautiful of form and [a]face, and when her father and her mother died, Mordecai took her as his own daughter.