(b) Controverted claims belonging to claimants residing in this state may either be proved in the domiciliary state as provided by the law of that state, or if ancillary proceedings have been commenced in this state, be proved in those proceedings. In the event that any such claimant elects to prove his claim in this state, he shall file his claim with the ancillary receiver and shall give notice in writing to the receiver in the domiciliary state, either by registered mail or by personal service at least forty days prior to the date set for hearing. The notice shall contain a concise statement of the amount of the claim, the facts on which the claim is based, and the priorities asserted, if any. If the domiciliary receiver within thirty days after the giving of such notice shall give notice in writing to the ancillary receiver and to the claimant, either by registered mail or by personal service, of his intention to contest such claim, he shall be entitled to appear or to be represented in any proceeding in this state involving adjudication of the claim. The final allowance of the claim by the courts of this state shall be accepted as conclusive as to its amount and shall also be accepted as conclusive as to its priority, if any, against special deposits or other security located within this state.