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If they had a green card and worked from the US that would make them a tax resident of the US right? How can they claim any Foreign Tax Credit if they were physically in the US. My understanding is that they would have to file all taxes in the US and claim a tax credit from the foreign country which has incorrectly withheld taxes, in this case Kazakhstan?

Also they would have to pay Social Security and Medicare taxes unless there is a agreement between the two countries?