  Spatially resolved integral field spectroscopic maps in a sample of $532$ S0
galaxies from the MaNGA survey have unveiled the existence of inner rings
($\langle R\rangle\sim 1\,R_\mathrm{e}$) betraying ongoing star formation in a
number of these objects. Activity gradients averaged over bins of
galactocentric radius up to $\sim 1.5\,R_\mathrm{e}$ have been measured in the
subspace defined by the first two principal components of the optical spectra
of these galaxies. We find that the sign of the gradients is closely related to
the presence of such rings in the spectral maps, which are especially
conspicuous in the equivalent width of the H$\alpha$ emission line,
EW(H$\alpha$), with a fractional abundance
$\unicode{x2014}21\unicode{x2013}34\%\unicode{x2014}$ notably larger than that
inferred from optical images. While the numbers of S0s with positive, negative,
and flat activity gradients are comparable, star-forming rings are largely
found in objects for which quenching proceeds from the inside out, in good
agreement with predictions from cosmological simulations studying S0 buildup.
Assessment of these ringed structures indicates that their frequency increases
with the mass of their hosts, that they have shorter lifetimes in galaxies with
ongoing star formation, that they may feed on gas from the disks, and that the
local environment does not play a relevant role in their formation. We conclude
that the presence of inner rings in the EW(H$\alpha$) is a common phenomenon in
fully formed S0s, possibly associated with annular disk resonances driven by
weakly disruptive mergers preferentially involving a relatively massive primary
galaxy and a tiny satellite strongly bound to the former.
