  Fe II 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 MgII$\lambda2800$ emission, which is one of the lines used for black
hole mass measurements and cosmological applications. We use the 11-year
monitoring of the selected quasar HE 0413-4031 with the South African Large
Telescope (SALT) and we supplement this monitoring with the near-IR spectrum
taken with the SOAR telescope. A new redshift determination ($z=1.39117 \pm
0.00017$) using [OIII]$\lambda \lambda 4959,5007$ 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 Mg II
and UV Fe II emissions. The line characteristics and the time delay of the Mg
II 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. Hence
the FeII-emitting material is more distant than the MgII-emitting gas in HE
0413-4031 by $\sim 0.023$ pc (4700 AU). The inferred velocity shift of both Mg
II 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 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 H$\beta$ $R-L$ relations. While the new decomposition of the
spectrum is satisfactory, we see a need to create better Fe II templates using
the newest version of the code CLOUDY.
