We update the results of the nucleon axial-vector charge with the third ensemble of the PACS10 gauge configurations, which are generated by the PACS Collaboration at the
physical point with lattice volume larger than $(10\;{\rm fm})^4$ and three
different lattice spacings, 0.085 fm (coarse), 0.063 fm (fine) and 0.041 fm (superfine).
Although the results of the first two ensembles generated at the coarse and fine lattice spacings
are published, our study using the third one generated at the superfine lattice spacing is still underway. In this work, the low-energy relations arising from the partially conserved axial-vector current (PCAC) relation are also examined in terms of the nucleon three-point functions to verify whether the lattice QCD data correctly reproduces the physics in the continuum within the statistical accuracy.