First of all, 130 grams is not a small amount ... it is over 4 ounces!
It is a controlled substance in the US and he can be denied future entry to the US for drug trafficking.
He needs a lawyer to review his CBP file with him/you.
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I would have to agree with my colleague. retain an attorney to request and review the records and subsequently decide on next steps.
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This may cause your fiance issues. I agree with my colleagues, contact an attorney and decide next actions from there.
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Unfortunately his actual "innocence" will be difficult to prove as he probably signed a statement acknowleding his guilt. Our immigration law treats drug related crimes very seriously so it will be very difficult for him to obtain a visa in the future. If you decide to hire an immigration attorney, make sure they have extensive experience handling waivers.