We report an experimental study of miniband magnetoconduction in semiconducting InAs/GaSb superlattices. For samples with miniband widths below the longitudinal optical phonon energy we identify a new superlattice magnetophonon resonance (SLMPR) caused by resonant scattering of electrons across the mini-Brillouin zone. This new resonant feature arises directly from the superlattice dispersion and total magnetic quantisation (energetic decoupling) of the superlattice Landau level minibands.Semiconductor superlattices (SL's) comprise alternating layers of two or more semiconductor materials, leading to the formation of continuous energy bands in the growth direction called minibands. The reduced Brillouin zone and energy band width of the SL allows measurements that probe parameter spaces which are inaccessible in bulk semiconductors. Total quantisation of the superlattice energy scheme can be achieved by the application of a large magnetic field which suppresses inter-Landau level miniband (LLMB) scattering and allows the realisation of a 'quasi' 1-dimensional or quantum box SL (QBSL) regime. This has led to strong interest in the SL magnetoresistance and transport characteristics [1, 2, 3, 4, 5]. The SL miniband structure can be engineered such that in the QBSL regime optical phonon scattering is limited [6,7] by using narrow minigap and miniband widths, leaving only weak acoustic-phonon processes to dissipate the electron energy. In this report we investigate magnetotransport properties of InAs/GaSb superlattices in the miniband transport regime. In a previous publication [5] we investigated hot-electron magnetophonon resonance caused by the LO phonon mediated hopping between Landau Wannier-Stark states at low temperatures. In this report we study longitudinal magnetophonon resonances caused by the resonant emission/absorption of longitudinal optical (LO) phonons in the miniband transport regime for a range of SL structures at high tempertures. Through a systematic study using different miniband widths we identify a new form of magnetophonon resonance which provides evidence for the energetic de-coupling of SL Landau level minibands leading to suppression of optical phonon scattering.