US doesn’t recognize the PRC as the head of China

you're really good at being wrong

https://en.wikipedia.org/wiki/United_Nations_General_Assembly_Resolution_2758

The United Nations General Assembly Resolution 2758 was passed in response to the United Nations General Assembly Resolution 1668 that required any change in China's representation in the UN be determined by a two-thirds vote referring to Article 18[1] of the UN Charter. The resolution, passed on 25 October 1971, recognized the People's Republic of China (PRC) as "the only legitimate representative of China to the United Nations" and removed "the representatives of Chiang Kai-shek" from the United Nations.[2]