On the nature of GRB 050509b: a disguised short GRB

(shortened) Context: GRB GRB 050509b, detected by the \emph{Swift} satellite, is the first case where an X-ray afterglow has been observed associated with a short gamma-ray burst (GRB). Within the fireshell model, the canonical GRB light curve presents two different components: the proper-GRB (P-GRB) and the extended afterglow. [...] In particular, the traditionally called short GRBs can be either "genuine" short GRBs [...] or "disguised" short GRBs [...]. AIMS: We verify whether GRB 050509b can be classified as a "genuine" short or a "disguised" short GRB, in the fireshell model. Methods: We investigate two alternative scenarios. In the first, we start from the assumption that this GRB is a "genuine" short burst. In the second attempt, we assume that this GRB is a "disguised" burst. Results: If GRB 050509b were a genuine short GRB, there should initially be very hard emission which is ruled out by the observations. The analysis that assumes that this is a disguised short GRB is compatible with the observations. The theoretical model predicts a value of the extended afterglow energy peak that is consistent with the Amati relation. Conclusions: GRB 050509b cannot be classified as a "genuine" short GRB. The observational data are consistent with a "disguised" short GRB classification, i.e., a long burst with a weak extended afterglow "deflated" by the low density of the CBM. We expect that all short GRBs with measured redshifts are disguised short GRBs because of a selection effect: if there is enough energy in the afterglow to measure the redshift, then the proper GRB must be less energetic than the afterglow. The Amati relation is found to be fulfilled only by the extended afterglow excluding the P-GRB.