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.
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