We show that triplet pairing correlations are generated in purely s-waves superfluids whenever population imbalance enforces anisotropic Fulde-Ferrell (FF) or inhomogeneous Larkin-Ovchinikov (LO) states. The same set of quasiparticle states contributes to the triplet component and to the polarization, thus spatially correlating them. In the LO case, this set forms a narrow band of Andreev states centered on the nodes of the s-wave order parameter. This picture naturally provides a unifying

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... nation of previous findings that attractive p-wave interaction stabilizes FFLO states. We also study a similar triplet mixing which occurs when a balanced two-component system displays FFLO type oscillations due to a spin-dependent optical lattice. We discuss how this triplet component can be measured in systems of ultra-cold atoms using a rapid ramp across a p-wave Feshbach resonance. This should provide a smoking gun signature of FFLO states.