  Magnetic fields in the stellar interiors are key candidates to explain
observed core rotation rates inside solar-like stars along their evolution.
Recently, asteroseismic estimates of radial magnetic field amplitudes near the
hydrogen-burning shell (H-shell) inside about 24 red-giants (RGs) have been
obtained by measuring frequency splittings from their power spectra. Using
general Lorentz-stress (magnetic) kernels, we investigated the potential for
detectability of near-surface magnetism in a 1.3 $M_{\odot}$ star of
super-solar metallicity as it evolves from a mid sub-giant to a late sub-giant
into an RG. Based on these sensitivity kernels, we decompose an RG into three
zones - deep core, H-shell, and near-surface. The sub-giants instead required
decomposition into an inner core, an outer core, and a near-surface layer.
Additionally, we find that for a low-frequency g-dominated dipolar mode in the
presence of a typical stable magnetic field, ~25% of the frequency shift comes
from the H-shell and the remaining from deeper layers. The ratio of the
subsurface tangential field to the radial field in H-burning shell decides if
subsurface fields may be potentially detectable. For p-dominated dipole modes
close to $\nu_\rm{max}$, this ratio is around two orders of magnitude smaller
in subgiant phases than the corresponding RG. Further, with the availability of
magnetic kernels, we propose lower limits of field strengths in crucial layers
in our stellar model during its evolutionary phases. The theoretical
prescription outlined here provides the first formal way to devise inverse
problems for stellar magnetism and can be seamlessly employed for slow
rotators.
