The Qing Dynasty annexed the island but was forced to give it up to the Japanese after the Sino-Japanese war. Their historical claim is debatable, but so is the RoC's occupation, imo.
This is as stupid as saying ROC is still a member of the UN simply because it is recognised by the UN chapter as a founding member of UN and permanent member of the UNSC.
How is this stupid? The PRC existed when Taiwan was given to the ROC. The borders (i.e. the real ones not the imaginary ones referenced by PRC and ROC laws) between the PRC and the ROC are unchanged in the last 69 years. So no it's quite clear that the Cairo declaration definitely does not support any claims of the PRC to Taiwan. Bringing up representation in the UN is irrelevant and if anything the only stupid thing said in this back and forth.