  Only indirect evidence of the role of magnetic braking in regulating
gravitational collapse and the formation of circumstellar disks was found from
observational work, such as compact disk sizes and the launching of
high-velocity collimated protostellar jets. More direct tests of the magnetic
braking shaping the angular momentum (AM) of the gas in Class 0 protostars are
crucially needed. In the present work we have used non-ideal MHD models of
protostellar collapse and synthetic observations of molecular gas spectral
emission that we analyze to test whether possible kinematic signatures of the
magnetic braking in the gas velocity field can be captured from maps of the
molecular gas emission in protostellar envelopes. By comparing the 3D Specific
AM of models with varying turbulent energy and magnetization, we show that, in
the numerical models of protostellar evolution explored, the increase in
magnetization and its consequences on the spatial redistribution of SAM
modifies the shapes of the radial profiles of SAM. We show that widely used
observational methods fail to quantitatively capture the magnitude of SAM of
the gas in protostellar envelopes, and that no method allows to measure the
differences in radial evolution of SAM due to different magnetization at all
envelope radii. This is especially true in the more magnetized cases. However,
our analysis suggests that the detection of symmetric patterns and organized
velocity fields, in the moment-1 maps of the molecular line emission as well as
monotonous radial profiles of the SAM showing a power-law decline, should be
suggestive of a less magnetized scenario. Protostellar cores where efficient
magnetic braking is at work are more likely to present a highly asymmetric
velocity field, and more prone to show complex radial profiles of their
specific angular momentum measured in the equatorial plane.
