We investigate a conjecture used in recent experiments to reconstruct the complete dynamics of Fano autoionization processes out of measured spectral amplitudes [Gruson et al., Science 354, 734 (2016); Beaulieu et al., Science 358, 1288 (2017); Busto et al., J. Phys. B: At. Mol. Opt. Phys. 51, 044002 (2018)]. The validity of the conjecture is established analytically within the formalism of Fano, and tested numerically on model atoms displaying adjustable autoionizing states. A general condition for which the conjecture is valid, beyond the Fano case, is then derived.