Context. Energy redistribution after a chemical reaction is one of the few mechanisms that can explain the diffusion and desorption of molecules which require more energy than the thermal energy available in quiescent molecular clouds (10 K). This energy distribution can be important in phosphorous hydrides, elusive yet fundamental molecules for interstellar prebiotic chemistry. Aims. Our goal with this study is to use state-of-the-art methods to determine the fate of the chemical energy in the simplest phosphorous hydride reaction. Methods. We studied the reaction dynamics of the P + H → PH reaction on amorphous solid water, a reaction of astrophysical interest, using ab initio molecular dynamics with atomic forces evaluated by a neural network interatomic potential. Results. We found that the exact nature of the initial phosphorous binding sites is less relevant for the energy dissipation process because the nascent PH molecule rapidly migrates to sites with higher binding energy after the reaction. Non-thermal diffusion and desorption after reaction were observed and occurred early in the dynamics, essentially decoupled from the dissipation of the chemical reaction energy. From an extensive sampling of on-site reactions, we constrained the average dissipated reaction energy within the simulation time (50 ps) to be between 50 and 70%. Most importantly, the fraction of translational energy acquired by the formed molecule was found to be mostly between 1 and 5%. Conclusions. Including these values, specifically for the test cases of 2% and 5% of translational energy conversion, in astrochemical models, reveals very low gas-phase abundances of PHx molecules and reflects that considering binding energy distributions is paramount to correctly merging microscopic and macroscopic modelling of non-thermal surface astrochemical processes. Finally, we found that PD molecules dissipate more of the reaction energy. This effect can be relevant for the deuterium fractionation and preferential distillation of molecules in the interstellar medium.