  Magnetic configurations, stable on the long term, appear to exist in various
evolutionary phases, from Main-Sequence stars to white dwarfs and neutron
stars. The large scale ordered nature of these fields, often approximately
dipolar, and their scaling according to the flux conservation scenario favor
the model of a fossil field (Duez et al. 2010). We make some first estimates of
the magnetic coupling between the stellar cores and the outer layers in red
giants and supergiants. Analytical expressions of the truncation radius of the
field coupling are established for a convective envelope and for a rotating
radiative zone with horizontal turbulence. The timescales of the internal
exchanges of angular momentum are considered.
  Numerical estimates are made on the basis of recent model grids. The direct
magnetic coupling of the core to the extended convective envelope of red giants
and supergiants appears unlikely. However, we find that the intermediate
radiative zone is fully coupled to the core during the He-burning and later
phases. This coupling is able to produce a strong spin down of the core of red
giants and supergiants, also leading to relatively slowly rotating stellar
remnants, like white dwarfs and pulsars. Some angular momentum is also
transferred to the outer convective envelope of red giants and supergiants
during the He-burning phase and later.
