Yes, of course! There is no way to recover a paper once it is burnt. How much ever you cool, the burnt paper, it won't become what it was before the burning.
Just to recap: if we cool water, we get ice. If we heat the ice, we get back water. The substance in water and ice is the same.

If we heat paper by burning it, we get burnt paper. But, cooling burnt paper doesn't give back the original paper. The substances in paper and burnt paper are not the same.