(a) A successor personal representative is entitled to demand, sue for, recover and collect all the estate of the decedent remaining unadministered, and may prosecute to final judgment any suit commenced by the former personal representative before the vacancy.
(b) No notice, process, or claim given to or served on the former personal representative need be given to or served on the successor in order to preserve any position or right the person giving the notice or filing the claim may thereby have obtained or preserved with reference to the former personal representative.
(c) Except as provided in subdivision (b) of Section 8442 (authority of administrator with will annexed) or as otherwise ordered by the court, the successor personal representative has the powers and duties in respect to the continued administration that the former personal representative would have had.