  Temperature induced transition of thin superconductor-ferromagnet-normal
(S/F/N) metal hybrid structure to in-plane Fulde-Ferrel-Larkin-Ovchinnikov
(FFLO) state is accompanied by vanishing of effective inverse magnetic field
penetration depth $\Lambda^{-1}$ (Phys. Rev. Lett. 121, 077002 (2018)). Here we
show that $\Lambda^{-1}$ goes to zero only in limit of zero magnetic field $H
\to 0$ and at any finite parallel $H$ or in-plane current $I$ it is finite and
positive in FFLO state which implies diamagnetic response. We demonstrate that
$\Lambda^{-1}$ has a nonmonotonic dependence on $H$ and $I$ not only in the
parameter range corresponding to the FFLO phase domain but also in its
vicinity. We find that for S/F/N/F/S structures with certain thicknesses of F
layers there is temperature, current and magnetic field driven transition to
and out of FFLO phase with a simultaneous jump of $\Lambda^{-1}$.
