Superconductor-Ferromagnet hybrid structures (SF) have attracted much interest in the last decades, due to a variety of interesting phenomena predicted and observed in these structures. One of them is the so-called inverse proximity effect. It is described by a spin polarization of Cooper pairs, which occurs not only in the ferromagnet (F), but also in the superconductor (S) yielding a finite magnetic moment $M_{text{S}}$ inside the superconductor. This effect has been predicted and experimentally studied. However, interpretation of the experimental data is mostly ambiguous. Here, we study theoretically the impact of the spin polarized Cooper pairs on the Josephson effect in an SFS junction. We show that the induced magnetic moment $M_{text{S}}$ does depend on the phase difference $varphi$ and therefore, will oscillate in time with the Josephson frequency $2eV/hbar$ if the current exceeds a critical value. Most importantly, the spin polarization in the superconductor causes a significant change in the Fraunhofer pattern, which can be easily accessed experimentally.
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