  Related to local systems with Stokes structure, we introduce two notions of
Stokes shells and extensions. Then, we apply them to study the Fourier
transform of holonomic $D$-modules on a complex projective line. Namely, we
explicitly describe the Stokes structure at infinity of the Fourier transform
of such $D$-modules as a successive extension of local systems with Stokes
structure which are constructed in terms of Stokes shells.
