  Dark matter may interact with the Standard Model through the kinetic mixing
of dark photons, $A'$, with Standard Model photons. Such dark matter will
accumulate in the Sun and annihilate into dark photons. The dark photons may
then leave the Sun and decay into pairs of charged Standard Model particles
that can be detected by the Alpha Magnetic Spectrometer. The directionality of
this "dark sunshine" is distinct from all astrophysical backgrounds, providing
an opportunity for unambiguous dark matter discovery by AMS. We perform a
complete analysis of this scenario including Sommerfeld enhancements of dark
matter annihilation and the effect of the Sun's magnetic field on the signal,
and we define a set of cuts to optimize the signal probability. With the three
years of data already collected, AMS may discover dark matter with mass 1 TeV
$\lesssim m_X \lesssim$ 10 TeV, dark photon masses $m_{A'} \sim \mathcal
O(100)$ MeV, and kinetic mixing parameters $10^{-10} \lesssim \varepsilon
\lesssim 10^{-8}$. The proposed search extends beyond existing beam dump and
supernova bounds, and it is complementary to direct detection, probing the same
region of parameter space for elastic dark matter, but potentially far more in
the case of inelastic dark matter.
