This is part of a study of dispersion of Halon and Halon-alternative fire extinguishment agents discharged from N2-pressurized vessels. As liquid agent exits from the vessel, thermodynamic and fluid-dynamic instabilities lead to flashing and break-up into a two-phase droplet/gaseous jet mixture. This occurs in a transition region relatively close to the vessel exit orifice/nozzle. Downstream, the agent jet is dispersed in the protected space. A model to simulate vessel discharge was developed previously. Using the output of this and thermodynamic and fluid-dynamic considerations of phenomena in the transition region, this paper develops a method for determining time-dependent boundary conditions at an initial section of the jet, downstream of the transition region. These boundary conditions can be used to simulate development and dispersal of the ensuing air/two-phase-agent jet. Applications of the methodology are presented.