  We investigate the specific angular momentum (sAM) $ j(<r)$ profiles of
intermediate redshift ($0.4<z<1.4$) star-forming galaxies (SFGs) in the
relatively unexplored regime of low masses (down to $M_\star\sim
10^8$M$_{\odot}$) and small sizes (down to $R_{\rm e}\sim 1.5$ kpc) and
characterize the sAM scaling relation and its redshift evolution. We have
developed a 3D methodology to constrain sAM profiles of the star-forming gas
using a forward modeling approach with \galpak{} that incorporates the effects
of beam smearing, yielding the intrinsic morpho-kinematic properties even with
limited spatial resolution data. Using mock observations from the TNG50
simulation, we find that our 3D methodology robustly recovers the SFR-weighted
$j(<r)$ profiles down to low effective signal-to-noise ratio (SNR) of
$\gtrapprox3$. We apply our methodology blindly to a sample of 494
\OII{}-selected SFGs in the MUSE Ultra Deep Field (UDF) 9~arcmin$^2$ mosaic
data, covering the unexplored $8<\log M_*/$M$_{\odot}<9$ mass range. We find
that the (SFR-weighted) sAM relation follows $j\propto M_\star^{\alpha}$ with
an index $\alpha$ varying from $\alpha=0.3$ to $\alpha=0.5$, from $\log
M_\star/$M$_{\odot}=8$ to $\log M_*/$M$_{\odot}=10.5$. The UDF sample supports
a redshift evolution consistent with the $(1+z)^{-0.5}$ expectation from a
Universe in expansion. The scatter of the sAM sequence is a strong function of
the dynamical state with $\log j|_{M_*}\propto 0.65 \times \log(V_{\rm
max}/\sigma)$ where $\sigma$ is the velocity dispersion at $2 R_{\rm e}$. In
TNG50, SFGs also form a $j-M_{\star}-(V/\sigma)$ plane but correlates more with
galaxy size than with morphological parameters. Our results suggest that SFGs
might experience a dynamical transformation before their morphological
transformation to becoming passive via either merging or secular evolution.
