  We investigate the environment and line of sight of the H0LiCOW lens
B1608+656 using Subaru Suprime-Cam and the Hubble Space Telescope (HST) to
perform a weak lensing analysis. We compare three different methods to
reconstruct the mass map of the field, i.e. the standard Kaiser-Squires
inversion coupled with inpainting and Gaussian or wavelet filtering, and
$\tt{Glimpse}$ a method based on sparse regularization of the shear field. We
find no substantial difference between the 2D mass reconstructions, but we find
that the ground-based data is less sensitive to small-scale structures than the
space-based observations. Marginalising over the results obtained with all the
reconstruction techniques applied to the two available HST filters F606W and
F814W, we estimate the external convergence, $\kappa_{\rm ext}$ at the position
of B1608+656 is $\kappa_{\rm ext} = 0.11^{+0.06}_{-0.04}$, where the error bars
corresponds respectively to the 16th and 84th quartiles. This result is
compatible with previous estimates using the number-counts technique,
suggesting that B1608+656 resides in an over-dense line of sight, but with a
completely different technique. Using our mass reconstructions, we also compare
the convergence at the position of several groups of galaxies in the field of
B1608+656 with the mass measurements using various analytical mass profiles,
and find that the weak lensing results favor truncated halo models.
