We analyze the multiplicity correlations between distant forward and backward rapidity regions in relativistic heavy-ion collisions in a superposition framework, where the particle production occurs through independent emission from correlated sources. This in principle allows for inferring information on the long-range forward-backward correlations of the sources in the earliest phase of the collision, based solely on the experimental information on the statistical features of the observed particle distributions. Our three-stage study incorporates the fluctuations of parton production in the early phase, the effect of intermediate hydrodynamic evolution, as well as fluctuations in the production of particles at freeze-out. We investigate the dependence of the results on the features of the overlaid distributions and hydrodynamics, as well as the centrality dependence. We analyze the existing data from the STAR Collaboration. Predictions for the forward-backward multiplicity correlations in Pb+Pb collisions to be analyzed at the LHC are also made.