Dear Querist
as per section 13 of CPC the Order passed by the Foreign Court shall not be conclusive.
Read the below mention section:-
13. When foreign judgment not conclusive.- A foreign judgment shall be conclusive as to any matter thereby directly adjudicated upon between the same parties or between parties under whom they or any of them claim litigating under the same title except,—
(a) where it has not been pronounced by a Court of competent jurisdiction;
(b) where it has not been given on the merits of the case;
(c) where it appears on the face of the proceedings to be founded on an incorrect view of international law or a refusal to recognize the law of India in cases in which such law is applicable;
(d) where the proceedings in which the judgment was obtained are opposed to natural justice;
(e) where it has been obtained by fraud;
(f) where it sustains a claim founded on a breach of any law in force in India.
You should immediately file an objection regarding the petition that the marriage has been solemnized as per Hindu Marriage Act-1955 in India hence the Court at US has no jurisdiction to decide the matter.
You may file a RCR petition in India through your Power of Attorney holder or left US and come to India and challenge the validity of US Court's Order.
My Opinion on your queries are as under:
1. How do I seek stay of divorce proceedings in US? Should I sign the stipulation mentioned by his attorney?
Opinion: Engage an advocate/Attorney in US and filed your objections, being an Indian and solemnization of Marriage as per Hindu Law the US Court has no jurisdiction to entertain the divorce petition filed by your Spouse.
2 If a hearing date comes up soon enough in US for declaration of assets, should I attend the hearing?
Opinion: It should be.
3. Can anyone file RCR on my behalf in India?
Opinion: Yes, Your power of attorney holder may file RCR petition on behalf of you in India.
4. Once RCR is filed, will hearing date be given immediately or will I need to come down again for the hearing.
Opinion: Your personal presance is not mandatory until the evidence/examination stage. next date of hearing shall be provided to your POA Holder on same day.
5. How much time it takes usually for RCR cases to be settled?
Opinion: If both the parties are not ready to settled their dispute amicably then more then 2 years.
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