FeII emission is a well-known contributor to the UV spectra of active galactic nuclei and the modeling of this part may affect the results obtained for the Mg II $ emission, which is one of the lines used for black hole mass measurements and cosmological applications. We tested different FeII emission models when modeling the UV emission of the intermediate-redshift quasar HE 0413-4031 to see how the use of a specific template affects the Mg II $ line properties and the measurement of the Mg II $ and UV Fe II time delays with respect to the continuum. We used the 11-year monitoring of the selected quasar HE 0413-4031 with the South African Large Telescope (SALT), and we supplemented this monitoring with the near-IR spectrum taken with the SOAR telescope, which gave access to the Hbeta $ and OIII 4959,5007$ emission lines at the rest frame and allowed for a precise measurement of the redshift. A new redshift determination ($z=1.39117 0.00017$) using OIII 4959,5007$ gave a very different value than the previous determination based only on the UV FeII pseudocontinuum ($z=1.3764$). It favors a different decomposition of the spectrum into MgII and UV FeII emissions. The line characteristics and the time delay of the MgII emission $ days) are not significantly affected. However, in comparison with the previous analysis, the rest-frame UV FeII time delay ($251^ km/s $ that is only slightly smaller than the MgII line FWHM. Hence the FeII-emitting material is more distant than the MgII-emitting gas in HE 0413-4031 by $ 0.023$ pc (4700 AU). The inferred velocity shift of both MgII and UV FeII lines with respect to the systemic redshift is now rather low, below 300 km $. In addition, we constructed an updated MgII radius-luminosity ($R-L$) relation from 194 sources, which is more than double the previous sample. The MgII $R-L$ relation is flatter than the UV FeII, optical FeII, and Hbeta $R-L$ relations. While the new decomposition of the spectrum is satisfactory, we see a need to create better FeII templates using the newest version of the code CLOUDY