The formation processes that led to the current Galactic stellar halo are still under debate. Previous studies have provided evidence for different stellar populations in terms of elemental abundances and kinematics, pointing to different chemical and star formation histories (SFHs). In the present work, we explore, over a broader range in metallicity (-2.2<[Fe/H]<+0.5), the two stellar populations detected in the first paper of this series from metal-poor stars in DR13 of the Apache Point Observatory Galactic Evolution Experiment (APOGEE). We aim to infer signatures of the initial mass function (IMF) and the SFH from the two {alpha}-to-iron versus iron abundance chemical trends for the most APOGEE-reliable {alpha}-elements (O, Mg, Si, and Ca). Using simple chemical-evolution models, we infer the upper mass limit (Mup) for the IMF and the star formation rate, and its duration for each population. Compared with the low-{alpha} population, we obtain a more intense and longer-lived SFH, and a top-heavier IMF for the high-{alpha} population.