Penetration of Cooper pairs from a superconducting layer to a ferromagnetic one in superconductor–ferromagnet contacts, known as a proximity effect, has been a subject of intensive research over the past few decades. At the beginning of the century, it became clear that the proximity effect is supplemented by a reverse influence of the magnetic material on the electronic subsystem of a superconductor, which manifests itself in the diffusion of magnetization through the interface of two metals. According to the former theory of the inverse proximity effect, the depth of such penetration is to be of the order of the coherence length in the superconductor. This phenomenon has been indeed observed, but detailed experiments, in particular neutron and muon scatterings, have revealed magnetic correlations at significantly greater distances. To explain the findings, a theory of the electromagnetic proximity effect is proposed, according to which the disproportion between electrons with different spin directions extends into a type-II superconductor at distances of the order of the London penetration depth. In this paper, we present experimental measurements of current-voltage characteristics of Josephson ferromagnet/superconductor–barrier–superconductor junctions confirming existence of the electromagnetic proximity effect in contacts formed by an ultrathin lead film—a type-II superconductor with a ferromagnetic nickel. Moreover, we first observed an oscillating dependence of the critical current of a Ni/Pb/Sn–oxide barrier–Pb junction on the Ni thickness, which indicates the presence of spatial oscillations of the superconducting order parameter in the Pb film predicted by the FFLO theory in mid-1960s.