The positron-hydrogen collision problem in weakly coupled plasma environment has been investigated by applying a formulation of the three-body collision problem in the form of coupled multi-channel two-body Lippmann-Schwinger equations. The interactions among the charged particles in the plasma have been represented by Debye-Huckel potentials. A simple variational hydrogenic wave function has been employed to calculate the partial-wave scattering amplitude. Plasma screening effects on various possible mode of fragmentation of the system e++H(1s) during the collision, such as 1s→1s and 2s→2s elastic collisions, 1s→2s excitation, positronium formation, elastic proton-positronium collisions, have been reported. Furthermore, a detailed study has been made on differential and total cross sections of the above processes in the energy range 13.6-350 eV of the incident positron.