  The generation of simulated convergence maps is of key importance in fully
exploiting weak lensing by Large Scale Structure (LSS) from which cosmological
parameters can be derived. In this paper we present an extension of the
PINOCCHIO code which produces catalogues of dark matter haloes so that it is
capable of simulating weak lensing by LSS. Like WL-MOKA, the method starts with
a random realisation of cosmological initial conditions, creates a halo
catalogue and projects it onto the past-light-cone, and paints in haloes
assuming parametric models for the mass density distribution within them. Large
scale modes that are not accounted for by the haloes are constructed using
linear theory. We discuss the systematic errors affecting the convergence power
spectra when Lagrangian Perturbation Theory at increasing order is used to
displace the haloes within PINOCCHIO, and how they depend on the grid
resolution. Our approximate method is shown to be very fast when compared to
full ray-tracing simulations from an N-Body run and able to recover the weak
lensing signal, at different redshifts, with a few percent accuracy. It also
allows for quickly constructing weak lensing covariance matrices, complementing
PINOCCHIO's ability of generating the cluster mass function and galaxy
clustering covariances and thus paving the way for calculating cross
covariances between the different probes. This work advances these approximate
methods as tools for simulating and analysing surveys data for cosmological
purposes.
