  We derive the complete super-sample covariance (SSC) of the matter and weak
lensing convergence power spectra using the power spectrum response formalism
to accurately describe the coupling of super- to sub-survey modes. The SSC term
is completely characterized by the survey window function, the nonlinear matter
power spectrum and the full first-order nonlinear power spectrum response
function, which describes the response to super-survey density and tidal field
perturbations. Generalized separate universe simulations can efficiently
measure these responses in the nonlinear regime of structure formation, which
is necessary for lensing applications. We derive the lensing SSC formulae for
two cases: one under the Limber and flat-sky approximations, and a more general
one that goes beyond the Limber approximation in the super-survey mode and is
valid for curved sky applications. Quantitatively, we find that for sky
fractions $f_{\rm sky} \approx 0.3$ and a single source redshift at $z_S=1$,
the use of the flat-sky and Limber approximation underestimates the total SSC
contribution by $\approx 10\%$. The contribution from super-survey tidal fields
to the lensing SSC, which has not been included in cosmological analyses so
far, is shown to represent about $5\%$ of the total lensing covariance on
multipoles $\ell_1,\ell_2 \gtrsim 300$. The SSC is the dominant off-diagonal
contribution to the total lensing covariance, making it appropriate to include
these tidal terms and beyond flat-sky/Limber corrections in cosmic shear
analyses.
