  TIC137608661/TYC4544-2658-1/FBS0938+788 is a new sdBV+dM reflection-effect
binary discovered by the TESS space mission with an orbital period of 7.21
hours. In addition to the orbital frequency and its harmonics, the Fourier
transform of TIC137608661 shows many g-mode pulsation frequencies from the sdB
star. The amplitude spectrum is particularly simple to interpret as we
immediately see several rotational triplets of equally spaced frequencies. The
central frequencies of these triplets are equally spaced in period with a mean
period spacing of 270.12 s, corresponding to consecutive l=1 modes. From the
mean frequency spacing of 1.25 {\mu}Hz we derive a rotation period of 4.6 days
in the deep layers of the sdB star, significantly longer than the orbital
period. Among the handful of sdB+dM binaries for which the sdB rotation was
measured through asteroseismology, TIC137608661 is the non-synchronized system
with both the shortest orbital period and the shortest core rotation period.
Only NY Vir has a shorter orbital period but it is synchronized. From a
spectroscopic follow-up of TIC137608661 we measure the radial velocities of the
sdB star, determine its atmospheric parameters, and estimate the rotation rate
at the surface of the star. This measurement allows us to exclude synchronized
rotation also in the outer layers and suggests a differential rotation, with
the surface rotating faster than the core, as found in few other similar
systems. Furthermore, an analysis of the spectral energy distribution of
TIC137608661, together with a comparison between sdB pulsation properties and
asteroseismic models, gives us further elements to constrain the system.
