Rav Moshe Shternbuch: Does A Son-in-Law Inherit A Rabbinic Position?
With regard to sons-in-law says Rav Shternbuch (3:460), the Rema in his tshuvos says that a son-in-law has the same Halacha as a son when it comes to inheriting a rabbinic position. The Avodas HaGershuni argues and says that since the daughter can never inherit the position the son-in-law has no claim. Rav Shternbuch holds that the inheriting a position is not based on the real Din of "Yerusha" like by money, rather it is just a way to honor the previous Rav by having his descendants continue to hold his position. Therefore son-in-laws should have the rights to the position over others if they are qualified because this will also honor the previous Rav.
He distinguishes between a Rabbi who is the boss of a shul and a Rabbi hired by a committee. The prior has a Din of a Rabbi in this issue and the latter is simply an employee. Another distinction he makes is between a Rav who paskens Shailos and is a Talmid Chochom versus a pulpit Rabbi whose main purpose is to deliver interesting speeches where the congregation has the right to decide whose speeches they would like to hear and not be bound by inheritance laws.
Important Note: Our only goal is to introduce a interesting Sheilah and not pasken Halacha. We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. Please also understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.