We investigate theoretically the circular polarization signals induced by the Zeeman effect in the Fe II lines of the 279.3-280.7 nm spectral range of the CLASP2 space experiment and their suitability to infer solar magnetic fields. To this end, we use a comprehensive Fe II atomic model to solve the problem of the generation and transfer of polarized radiation in semiempirical models of the solar atmosphere, comparing the region of formation of the Fe II spectral lines with those of the Mg II h and k and the Mn I resonance lines. These are present in the same near-ultraviolet (near-UV) spectral region and allowed the mapping of the longitudinal component of the magnetic field (B L) through several layers of the solar chromosphere in an active region plage. We compare our synthetic intensity profiles with observations from the IRIS and CLASP2 missions, proving the suitability of our model atom to characterize these Fe II spectral lines. The CLASP2 observations show two Fe II spectral lines at 279.79 and 280.66 nm with significant circular polarization signals. We demonstrate the suitability of the weak-field approximation applied to the Stokes I and V profiles of these Fe II lines to infer B L in the plage atmosphere. We conclude that the near-UV spectral region of CLASP2 allows us to determine B L from the upper photosphere to the top of the chromosphere of active region plages.