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He can file for a divorce anywhere, the question is whether the divorce will be recognized in the US. A divorce decree issued in a foreign country generally is recognized in many states in the United States on the basis of cooperation between the courts provided both parties to the divorce received adequate notice, provided one of the parties was a legal resident in the foreign nation at the time of the divorce. Many state courts which have addressed the question of a foreign divorce where both parties participate in the divorce proceedings but neither obtains residence there have followed the view that such a divorce invalid. This prohibited divorces of convenience for avoiding taxes in the U.S.
The validity of the divorce will depend on whether the process in obtaining the divorce was in conformance to Saudi law and provided you with an opportunity to participate. If a divorce is given it validity may still be challenged if adequate documentation is not produced by your husband to substantiate the diveorce. If you husband proceeds you should require the paperwork and have an attorney review it to assure its validity.
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Please be aware that my answer is not legal advice, it is merely information and no attorney client relationship has been formed. You should always contact a local attorney for legal advice.