  During a coordinated campaign which took place in May 2001, a C-class flare
was observed both with SOHO instruments and with the Dunn Solar Telescope of
the National Solar Observatory at Sacramento Peak. In two previous papers we
have described the observations and discussed some dynamical aspects of the
earlier phases of the flare, as well as the helium line formation in the active
region prior to the event. Here we extend the analysis of the helium line
formation to the later phases of the flare in two different locations of the
flaring area. We have devised a new technique, exploiting all available
information from various SOHO instruments, to determine the spectral
distribution of the photoionizing EUV radiation produced by the corona
overlying the two target regions. In order to find semiempirical models
matching all of our observables, we analyzed the effect on the calculated
helium spectrum both of A(He) (the He abundance) and of the uncertainties in
the incident EUV radiation (level and spectral distribution). We found that the
abundance has in most cases (but not in all) a larger effect than the coronal
back-radiation. The result of our analysis is that, considering the error of
the measured lines, and adopting our best estimate for the coronal EUV
illumination, the value A(He)=0.075 +/- 0.010 in the chromosphere (for T>6300
K) and transition region yields reasonably good matches for all the observed
lines. This value is marginally consistent with the most commonly accepted
photospheric value: A(He)=0.085.
