Legal Question in Insurance Law in California

Your question is unclear. However, if there is a successor-in-interest, then yes. See CCP 377.30 which states:

A cause of action that survives the death of the person entitled to commence an action or proceeding passes to the decedent's successor in interest, subject to Chapter 1 (commencing with Section 7000) of Part 1 of Division 7 of the Probate Code, and an action may be commenced by the decedent's personal representative or, if none, by the decedent's successor in interest.

If there is an executor appointed then there is presumably an open probate. Hence, the UM claim must also be submitted to the probate court.