Cal. Prob. Code § 13107.5

Where the money or property claimed in an affidavit or declaration executed under this chapter is the subject of a pending action or proceeding in which the decedent was a party, the successor of the decedent shall, without procuring letters of administration or awaiting probate of the will, be substituted as a party in place of the decedent by making a motion under Article 3 (commencing with Section 377.30) of Chapter 4 of Title 2 of Part 2 of the Code of Civil Procedure. The successor of the decedent shall file the affidavit or declaration with the court when the motion is made. For the purpose of Article 3 (commencing with Section 377.30) of Chapter 4 of Title 2 of Part 2 of the Code of Civil Procedure, a successor of the decedent who complies with this chapter shall be considered as a successor in interest of the decedent.