  We study AB oscillations of transition temperature, paraconductivity and
specific heat of thin ring in the regime of inhomogeneous Larkin - Ovchinnikov
- Fulde - Ferrell superconducting state. We found that in contrast to uniform
superconductivity magnetic flux might increase the critical temperature of LOFF
state. Degeneracy of the inhomogeneous superconducting state reveals in double
peak structure of AB oscillations.
