  Open quantum systems exhibiting initial system-environment correlations are
notoriously difficult to simulate. We point out that given a sufficiently long
sample of the exact short-time evolution of the open system dynamics, one may
employ transfer tensors for the further propagation of the reduced open system
state. This approach is numerically advantageous and allows for the simulation
of quantum correlation functions in hardly accessible regimes. We benchmark
this approach against analytically exact solutions and exemplify it with the
calculation of emission spectra of multichromophoric systems as well as for the
reverse temperature estimation from simulated spectroscopic data. Finally, we
employ our approach for the detection of spectral signatures of
electromagnetically-induced transparency in open three-level systems.
