The dynamics of the amphiphilic semifluorinated F(CF2)12(CH2)12H (F12H12) alkane that undergoes two condensed phase transitions have been investigated by Brillouin light spectroscopy, shear rheometry, small- (SAXS) and wide-angle (WAXS) X-ray scattering, and thermodynamic PVT measurements. The solid (I)-solid (II) transition (Ts) is marked by a stronger temperature dependence of the sound velocity in phase II and by a 2 orders of magnitude drop of the shear modulus. Between the Ts and the melting transition (Tm), the presence of two phonons implies a coexistence of solid (II) and amorphous (liquid) regions in the submicrometer range at thermal equilibrium as revealed by the SAXS pattern of a single reflection superimposed on a very broad amorphous halo. This intriguing finding of a transient, very slow (over 10 h) solid/liquid coexistence within phase II is rationalized by a two-stage mechanism for melting of the smectic phase (II) of F12H12. A refinement of the known packing motifs for the two solid-state structures is proposed.