  We present a simple method to accurately infer line of sight (LOS) integrated
lensing effects for galaxy scale strong lens systems through image
reconstruction. Our approach enables us to separate weak lensing LOS effects
from the main strong lens deflector. We test our method using mock data and
show that strong lens systems can be accurate probes of cosmic shear with a
precision on the shear terms of $\pm 0.003$ (statistical error) for an HST-like
dataset. We apply our formalism to reconstruct the lens COSMOS 0038+4133 and
its LOS. In addition, we estimate the LOS properties with a halo-rendering
estimate based on the COSMOS field galaxies and a galaxy-halo connection. The
two approaches are independent and complementary in their information content.
We find that when estimating the convergence at the strong lens system,
performing a joint analysis improves the measure by a factor of two compared to
a halo model only analysis. Furthermore the constraints of the strong lens
reconstruction lead to tighter constraints on the halo masses of the LOS
galaxies. Joint constraints of multiple strong lens systems may add valuable
information to the galaxy-halo connection and may allow independent weak
lensing shear measurement calibrations.
