The linear polarizability, first and second hyperpolarizabilities of the asymmetric unit of DAPSH crystal are studied and compared with available experimental results. The polarization effects are included using an iterative polarization procedure, which ensures the convergence of the dipole moment of DAPSH embedded within a polarization field generated by the surrounding asymmetric units whose atomic sites are considered as point charges. We estimate macroscopic susceptibilities from the results of the polarized asymmetric units in the unit cell, considering the significant contribution of the electrostatic interactions in crystal packing. The results show that the influence of the polarization effects leads to a marked decrease of the first hyperpolarizability, compared with the respective isolated counterpart, which improves the concordance with the experiment. There is a minor influence of polarization effects on the second hyperpolarizability but our estimated result for the third-order susceptibility, related to the NLO process of the intensity dependent refractive index, is significant as compared with the results for other organic crystals, such as chalcone-derivatives. In addition, supermolecule calculations are conducted for explicit dimers in presence of the electrostatic embedding to illustrate the role played by the electrostatic interactions in the hyperpolarizabilities of the DAPSH crystal.