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Fe II emission is a well-known contributor to the UV spectra of activegalactic nuclei and the modeling of this part may affect the results obtainedfor the MgII$\lambda2800$ emission, which is one of the lines used for blackhole mass measurements and cosmological applications. We use the 11-yearmonitoring of the selected quasar HE 0413-4031 with the South African LargeTelescope (SALT) and we supplement this monitoring with the near-IR spectrumtaken with the SOAR telescope. A new redshift determination ($z=1.39117 \pm0.00017$) using [OIII]$\lambda \lambda 4959,5007$ gave a very different valuethan the previous determination based only on the UV FeII pseudocontinuum($z=1.3764$). It favors a different decomposition of the spectrum into Mg IIand UV Fe II emissions. The line characteristics and the time delay of the MgII emission ($224^{+21}_{-23}$ days) are not significantly affected. However,in comparison with the previous analysis, the rest-frame UV FeII time delay($251^{+9}_{-7}$ days) is consistent with the inferred UV FeII line FWHM of$4200\,{\rm km/s}$ that is only slightly smaller than the MgII line FWHM. Hencethe FeII-emitting material is more distant than the MgII-emitting gas in HE0413-4031 by $\sim 0.023$ pc (4700 AU). The inferred velocity shift of both MgII and UV Fe II lines with respect to the systemic redshift is now rather low,below 300 km s$^{-1}$. In addition, we construct an updated MgIIradius-luminosity ($R-L$) relation from 194 sources, which is more than doublethe previous sample. The MgII $R-L$ relation is flatter than the UV FeII,optical FeII, and H$\beta$ $R-L$ relations. While the new decomposition of thespectrum is satisfactory, we see a need to create better Fe II templates usingthe newest version of the code CLOUDY.

UV Fe II emission model of HE 0413-4031 and its relation to broad-line time delays