PbS quantum dots (QDs) of different sizes capped with short (NH4)3AsS3 inorganic ligands are produced via ligand exchange processes from oleate-capped PbS QDs. The solid-state photophysical properties of the control organic-capped and the inorganic-ligand-capped QDs are investigated to determine their potential for optoelectronic applications. Ultrafast transient transmission shows that in the oleate-capped QDs, carrier recombination at sub-nanosecond scales occurs via Auger recombination, traps, and surface states. At longer times, intense signals associated with radiative recombination are obtained. After ligand exchange, the QDs become decorated with (NH4)3AsS3 complexes and relaxation is dominated by efficient carrier transfer to the ligand states on timescales as fast as ≈2 ps, which competes with carrier thermalization to the QD band edge states. Recombination channels present in the oleate-capped QDs, such as radiative and Auger recombination, appear quenched in the inorganic-capped QDs. Evidence of efficient carrier trapping at shallow ligand states, which appears more intense under excitation above the (NH4)3AsS3 gap, is provided. A detailed band diagram of the various relaxation and recombination processes is proposed that comprehensively describes the photophysics of the QD systems studied.