A theory of dynamic polarization of the nuclear spin system via optically oriented charge carriers in lead halide perovskites is developed and compared with the experiments performed on a FA0.9Cs0.1PbI2.8Br0.2 crystal. The spin Hamiltonians of the electron and hole hyperfine interaction with the nuclear spins of lead and halogen are derived. The hyperfine interaction of the halogen spins with charge carriers is shown to be anisotropic and depending on the position of the halogen nucleus in the cubic elementary cell. The quadrupole splitting is absent for the lead spins, but plays an important role for the halogen spins and affects their dynamic polarization by charge carriers. The Overhauser fields of the dynamically polarized nuclei are calculated as functions of the tilting angle of an external magnetic field and compared with the experimentally measured angular dependence of the Hanle effect. The comparison of the theoretical model with the experimental data reveals an enhanced spin polarization of the lead nuclei, whose mean spin exceeds several times the mean spins of localized electrons and holes. This unexpectedly strong spin polarization is explained by the interaction of the lead nuclei with excitons having a high degree of spin orientation because of their short lifetime after excitation by circularly polarized light. The dynamic polarization of the quadrupole-split halogen spins manifests itself via the magnetic field they produce at the lead nuclei. This field maintains the magnetization of the lead nuclei at zero external magnetic field. The dynamics of the nuclear spin polarization is measured under optical pumping and in the dark, yielding a nuclear spin-lattice relaxation time on the order of 10 seconds. © 2026 American Physical Society