In this third paper of a series, we discuss the physics of the population of accelerated particles in the precursor of an unmagnetized, relativistic collisionless pair shock. In particular, we provide a theoretical estimate of their scattering length l_{scatt}(p) in the self-generated electromagnetic turbulence, as well as an estimate of their distribution function. We obtain l_{scatt}(p)≈γ_{p}ε_{B}^{-1}(p/γ_{∞}mc)^{2}c/ω_{p}, with p the particle momentum in the rest frame of the shock front, ε_{B} the strength parameter of the microturbulence, γ_{p} the Lorentz factor of the background plasma relative to the shock front, and γ_{∞} its asymptotic value outside the precursor. We compare this scattering length to large-scale PIC simulations and find good agreement for the various dependencies.