We present an investigation of the dynamics of the inter-Landau-level (LL) excitations of a two-dimensional electron gas (2DEG) in large magnetic fields using coherent time-resolved nonlinear spectroscopy. The results are compared directly with measurements on undoped quantum wells. We observe time-dependent Coulomb coupling between the LL's induced by the 2DEG that induces a large transfer of oscillator strength to the lowest LL. The time dependence of the nonlinear response reveals non-Markovian and memory effects of the photoexcited system that cannot be understood in terms of the random phase approximation. We introduce a theoretical approach that treats the interactions of the magnetoexcitons with the 2DEG excitations and qualitatively accounts for the most salient experimental results in terms of shake-up of the 2DEG.