The upper critical magnetic field Hc2 in thin film ferromagnet-superconductor-ferromagnet trilayer spin-valve cores is studied experimentally and theoretically in geometries perpendicular and parallel to the heterostructure surface. The series of samples with variable thicknesses d F1 of the bottom and dF2 of the top Cu41Ni 59 ferromagnet (F) layers are prepared in a single run, utilizing a wedge deposition technique. The critical field Hc2 is measured in the temperature range 0.4-8 K and for magnetic fields up to 9 T. A transition from oscillatory to reentrant behavior of the superconducting transition temperature versus F-layer thickness, induced by an external magnetic field, has been observed for the first time. In order to properly int...