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If you are a resident alien (green card holder), then someone in your situation must declare income from abroad. See HERE.
There is a penalty if caught - the penalty is equal to 20 percent of the underpayment. The penalty becomes 40 percent for any portion of the underpayment that is attributable to an undisclosed no-neconomic substance transaction, or, an undisclosed foreign financial asset transaction.
Criminal charges may also be filed for non-declarations, but this is rare.
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