We propose a picture for the magnetic properties of superconductor/ferromagnet (S/F) heterostructures based on Nb and permalloy (Py: Fe_{20}Ni_{80}). By measuring the magnetic moment as a function of the temperature in S/F/S trilayers for different thicknesses of the middle F layer, we give evidence of the presence of a magnetic stray field of the F layer. For values of F-layer thickness below a threshold, we establish a correlation between the magnetic measurements of the S/F/S trilayers and the anomalous magnetic dependence of the critical current in S/insulator/thin superconducting film/F/S (SIsFS) Josephson junctions (JJs). These complementary investigations provide a self-consistent method to fully characterize S/F heterostructures and possibly demonstrate effects arising from the mutual interactions between ferromagnetism and superconductivity. A shift in the Fraunhofer critical current oscillations has been observed in the opposite direction to the one commonly observed in JJs with F barriers, as it has been recently predicted by inverse and electromagnetic proximity theories. This inverse memory effect is relevant for the design of these heterostructures as memory cells and spintronic devices.
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