The upper critical magnetic field H_{c2} in thin-film FSF 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 o
f the bottom and of the top Cu_{41}Ni_{59} F-layers are prepared in a single run, utilizing a wedge deposition technique. The critical field H_{c2} is measured in the temperature range $0.4-8$ K and for magnetic fields up to 9 Tesla. A transition from oscillatory to reentrant behavior of the superconducting transition temperature versus F-layers thickness, induced by an external magnetic field, has been observed for the first time. In order to properly interpret the experimental data, we develop a quasiclassical theory, enabling one to evaluate the temperature dependence of the critical field and the superconducting transition temperature for an arbitrary set of the system parameters. A fairly good agreement between our experimental data and theoretical predictions is demonstrated for all samples, using a single set of fit parameters. This confirms adequacy of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) physics in determining the unusual superconducting properties of the studied Cu_{41}Ni_{59}/Nb/Cu_{41}Ni_{59} spin-valve core trilayers.
