  We provide a systematic study of the position-dependent correlation function
in weak lensing convergence maps and its relation to the squeezed limit of the
three-point correlation function (3PCF) using state-of-the-art numerical
simulations. We relate the position-dependent correlation function to its
harmonic counterpart, i.e., the position-dependent power spectrum or
equivalently the integrated bispectrum. We use a recently proposed improved
fitting function, BiHalofit, for the bispectrum to compute the theoretical
predictions as a function of source redshifts. In addition to low redshift
results ($z_s=1.0-2.0$) we also provide results for maps inferred from lensing
of the cosmic microwave background, i.e., $z_s=1100$. We include a {\em
Euclid}-type realistic survey mask and noise. In agreement with the recent
studies on the position-dependent power spectrum, we find that the results from
simulations are consistent with the theoretical expectations when appropriate
corrections are included.
