We present a simple method for simulating isothermal compressible two-phase flows with mass transfer. The convective part of the model is compatible with the Least Action Principle and the system is endowed with an entropy inequality which accounts for phase change terms and phasic pressure unbalance. A study of the system as a relaxed model of two equilibrium models is performed. This study allows the design of two-step relaxation-convection Finite-Volume discretization scheme which complies with the entropy balance of the model which drives the mass transfer phase-change process. Numerical results involving dynamical phase-change are presented.