Biot’s model is a multiphysics model that describes the interaction of a poroelastic material with its interstitial fluid flow. In this study, we focus on investigating the convergence behavior of a global-in-time iterative decoupled algorithm based on a three-field formulation. During each iteration, the algorithm involves solving a reaction-diffusion subproblem across the entire temporal domain, followed by resolving a Stokes subproblem over the same time interval. This algorithm is recognized for its ”partially parallel-in-time” property, enabling the implementation of a parallel procedure when addressing the Stokes subproblem. We establish its global convergence with a new technique by confirming that the limit of the sequence of numerical solutions of the global-in-time algorithm is the numerical solution of the fully coupled algorithm. Numerical experiments validate the theoretical predictions and underline the efficiency gained by implementing the parallel procedure within the proposed global-in-time algorithm.