The problem studied in this note refers to a substantial part of a larger system of partial differential equations modelingdiffusion and fast reaction of a gaseous speciesAin a reactive spherical porous region. We report on the local existence anduniqueness of weak solutions to the corresponding moving-boundary system containing two coupled mass-balance equationsin a moving annulus. Since the system incorporates an explicit description of the velocity of the moving boundary, ourformulation resembles to the one-phase Stefan-like problem with kinetic condition.