From your own link
Posted on: March 22, 2021 at 14:08:07 CT
Spanky KU
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"Above all, no formal notification needs to take place for the U.S. citizenship to be lost (for immigration purposes). One would simply perform such an act with the intention to relinquish U.S. citizenship. He/she could rightly claim to no longer be a U.S. citizen after performing that act."