We theoretically study internal inter-Landau-level spin-singlet and spin-triplet transitions of quasi-two-dimensional charged excitons X- in strong magnetic fields. We establish a novel exact selection rule that governs bound-to-bound transitions of charged mobile complexes in a uniform magnetic field. As an example, the bound-to-bound X- triplet transition to the next electron Landau level, which lies below the electron cyclotron resonance, is shown to be prohibited. The X- photoionizing transitions have a characteristic double-peak structure, which reflects the rich structure of the magnetoexciton continua in higher Landau levels.