  The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in
superconductors for which the orbital critical field exceeds the Pauli limit.
Here, we present angular-resolved specific-heat data of the
quasi-two-dimensional organic superconductor $\kappa$-(ET)$_2$Cu(NCS)$_2$, with
a focus on high fields in the regime of the FFLO transition. For an increasing
out-of-plane tilt of the applied magnetic field, which leads to an increase of
orbital contributions, we found that the nature of the superconducting
transition changes from second to first order and that a further transition
appears within the high-field superconducting phase. However, the
superconducting state above the Pauli limit is stable for field tilt of several
degrees. Since any finite perpendicular component of the magnetic field
necessarily leads to quantization of the orbital motion, the resulting vortex
lattice states compete with the modulated order parameter of the FFLO state
leading to complex high-field superconducting phases. By solving the linearized
self-consistency equation within weak-coupling BCS theory, we show that our
results are clear experimental evidence of an orbital-induced transformation of
the FFLO order-parameter into Abrikosov-like states of higher Landau levels.
