False claim to US citizenship, especially to gain an immigration benefit (entry into the US is a benefit) is one of the most serious violations of the immigration laws making one inadmissible for life.
It is on the level of having a conviction for homicide or trafficking in drugs, that is how serious it is taken under the laws.
There is no waiver for this charge of inadissibility under section 212(a) (6)(C)(ii) for such claims made after 1996.
Unfortunately, it would be unethical for me to tell you there is any defense to this charge, especially since it was made directly to a US Customs officer.
She will never be given an immigrant or non-immigrant visa unless some immigration reform law is passed which seems more than hopeless now. Congress has resisted immigration reform since 2001.
And despite Executive Action by the President, the Supreme Court last week said he was without authority to provide immigration relief, such action rested solely with the Congress.
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In the future, you may begin your questions with “FOR JUDITH” and I will be your personal immigration expert.