Infrared reflectivity spectra of cubic SrMnO$_{3}$ ceramics reveal 18 % stiffening of the lowest-frequency phonon below the antiferromagnetic phase transition occurring at T$_{N}$ = 233 K. Such a large temperature change of the polar phonon frequency is extraordinary and we attribute it to an exceptionally strong spin-phonon coupling in this material. This is consistent with our prediction from first principles calculations. Moreover, polar phonons become Raman active below T$_{N}$, although their activation is forbidden by symmetry in $Pmbar{3}m$ space group. This gives evidence that the cubic $Pmbar{3}m$ symmetry is locally broken below T$_{N}$ due to a strong magnetoelectric coupling. Multiphonon and multimagnon scattering is also observed in Raman spectra. Microwave and THz permittivity is strongly influenced by hopping electronic conductivity, which is caused by small non-stoichiometry of the sample. Thermoelectric measurements show room-temperature concentration of free carriers $n_{e}=$3.6 10$^{20}$ cm$^{-3}$ and the sample composition Sr$^{2+}$Mn$_{0.98}^{4+}$Mn$_{0.02}^{3+}$O$_{2.99}^{2-}$. The conductivity exhibits very unusual temperature behavior: THz conductivity increases on cooling, while the static conductivity markedly decreases on cooling. We attribute this to different conductivity of the ceramic grains and grain boundaries.
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