Complete conductivity spectra of a lithium ion conducting glass of composition B2O3-0.56Li2O - 0.45 LiBr have been taken at twelve temperatures from 173 K to 573 K, covering the frequency range from a few Hertz up to about 50 THz. For the first time, a separation of the hopping and vibrational contributions to the spectra has been performed. The resulting frequency dependent hopping conductivity displays a high-frequency plateau similar to those known to exist in crystalline solid electrolytes like RbAg4I5 and Na-β-alumina. In the dispersive regime of the conductivity, there is an increase of the apparent power-law exponent from p = 0.6 to q = 1.3. The spectra are evaluated by combined application of the jump relaxation model and the dynamic structure model. Besides the translational hopping of the lithium ions via the preferred Ā sites, more localized kinds of motion are also detected, viz., hops into the less favoured C̄ sites (and mostly back again) as well as smaller displacements of the ions within their local environment.