We report an unusual enhancement of the magnetic induction in single crystals of the magnetic superconductor RbEuFe4As4 , highlighting the interplay between superconducting and magnetic subsystems in this material. Contrary to the conventional Meissner expulsion of magnetic flux below the superconducting transition temperature, we observe a substantial boost of the magnetic flux density upon approaching the magnetic transition temperature, Tm. Direct imaging of the flux evolution with a magneto-optical technique, shows that the magnetic subsystem serves as an internal magnetic flux pump, drawing Abrikosov vortices from the surface, while the superconducting subsystem controls their conveyance into the bulk of the magnetic superconductor via a peculiar self-organized critical state.The co-existence of superconductivity and magnetism in the new family of rare-earth iron pnictides with high Tc and comparable magnetic Curie points [1-7], provides a rare glimpse into the interplay of these typically antithetical phases. Compared to the low-temperature magnetic superconductors, where weak magnetism accompany superconductivity only in a very narrow temperature window [8,9], in the new pnictides the superconducting and magnetic orders robustly coexist over a wide range of temperatures. For example, in phosphorus-doped EuFe2As2, the superconductivity appears below Tc~24K, while at the Curie point, Tm~19K, the Eu-spins order ferromagnetically in layers separated by the superconducting FeAs-sheets and align parallel to the c-axis [10]. Recent MFM studies have found that in this material the Meissner state coexists with very fine ferromagnetic domains that are smaller than the penetration depth and at lower temperatures transforms into a vortex-domain state [11,12].