It could pose a problem. The answer will depend upon more information regarding the outcome of the criminal case. He must disclose the arrest. He actually should have already disclosed the arrest on his application. He will also need to submit a certified copy of the certificate of disposition. This can be obtained from the criminal court where his case was adjudicated. You should strongly consider retaining an experienced immigration attorney to review the matter.
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Depends how much of marihuana and when in 1997.
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If he can't remember the court where he was charged (some people have horrible memories when it comes to things like this), he can always do an FBI records request. That is easy, inexpensive and usually pretty fast - it should give him the appropriate information of what court to look to in order to obtain certified copies of the charging document and final disposition. Good luck.