The crystal structure and lattice phonons of (BEDT-TTF)2I3 superconducting β-phase (where BEDT-TTF is bis-ethylen-dithio-tetrathiafulvalene) are computed and analyzed by the Quasi Harmonic Lattice Dynamics (QHLD) method. The empirical atom-atom potential is that successfully employed for neutral BEDT-TTF and for non superconducting α-(BEDT-TTF)2I3. Whereas the crystal structure and its temperature and pressure dependence are properly reproduced within a rigid molecule approximation, this has to be removed account for the specific heat data. Such a mixing between lattice and low-frequency intra-molecular vibrations also yields good agreement with the observed Raman and infrared frequencies. From the eigenvectors of the low-frequency phonons we calculate the electron-phonon coupling constants due to the modulation of charge transfer (hopping) integrals. The charge transfer integrals are evaluated by the extended Hückel method applied to all nearest-neighbor BEDT-TTF pairs in the ab crystal plane. From the averaged electron-phonon coupling constants and the QHLD phonon density of states we derive the Eliashberg coupling function α(ω)F (ω), which compares well with that experimentally obtained from point contact spectroscopy. The corresponding dimensionless coupling constant λ is found to be ∼ 0.4. 74.70. Kn,74.25.Kc