Addendum to `Threshold corrections to m(b) and the anti-b b ---> H0(i) production in CP-violating SUSY scenarios'

In hep-ph/0401024: ``Threshold corrections to $m_b$ and the $\bar{b}b\to H^0_i$ production in CP-violating SUSY scenarios'', we have pointed out that the production cross sections of the three neutral Higgs bosons through $\bar{b}b$ fusion can deviate substantially from those obtained in CP conserving scenarios, thanks to the nontrivial role played by the threshold corrections to $m_b$ combined with the CP-violating mixing in the neutral-Higgs-boson sector. The deviations are largest for values of the CP-violating phases that maximize the mixing among at least two of the three neutral Higgs bosons. We complement our previous work focussing explicitly on the values of masses and widths of the three neutral Higgs bosons in this region of parameter space. We then address the issue of whether the three different peaks in the invariant mass distribution of the Higgs-decay products can be experimentally disentangled at the LHC.