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We study the structure of the higher genus Gromov-Witten theory of the totalspace $K\mathbb{P}^{n-1}$ of the canonical bundle of the projective space$\mathbb{P}^{n-1}$. We prove the finite generation property for theGromov-Witten potential of $K\mathbb{P}^{n-1}$ by working out the details ofits cohomological field theory (CohFT). More precisely, we prove that theGromov-Witten potential of $K\mathbb{P}^{n-1}$ lies in an explicit polynomialring using the Givental-Teleman classification of the semisimple CohFTs.  In arXiv:2301.08389, we carried out a parallel study for$[\mathbb{C}^n/\mathbb{Z}_n]$ and proved that the Gromov-Witten potential of$[\mathbb{C}^n/\mathbb{Z}_n]$ lies in a similar polynomial ring. The mainresult of this paper is a crepant resolution correspondence for higher genusGromov-Witten theories of $K\mathbb{P}^{n-1}$ and$[\mathbb{C}^n/\mathbb{Z}_n]$, which is proved by establishing an isomorphismbetween the polynomial rings associated to $K\mathbb{P}^{n-1}$ and$[\mathbb{C}^n/\mathbb{Z}_n]$. This paper generalizes the works ofLho-Pandharipande arXiv:1804.03168 for the case of$[\mathbb{C}^3/\mathbb{Z}_3]$ and Lho arXiv:2211.15878 for the case$[\mathbb{C}^5/\mathbb{Z}_5]$ to arbitrary $n\geq 3$.

Higher Genus Gromov-Witten Theory of C^n/Z_n II: Crepant Resolution Correspondence