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⋆ ∼ 108 M⊙) and small sizes (down to Re ∼ 1.5 kpc), and we characterize the sAM scaling relation (i.e., Fall 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 GAlPAK3D 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 star formation rate (SFR)-weighted j̃⋆(<r) profiles down to a low effective signal-to-noise ratio of ⪆3. We applied our methodology blindly to a sample of 494 [O II]-selected SFGs in the MUSE Ultra Deep Field (UDF) 9 arcmin2 mosaic data, covering the unexplored 8 < log M⋆/M⊙ < 9 mass range. We find that the (SFR-weighted) sAM relation follows j̃⋆ ∝ M⋆α with an index α varying from α = 0.3 to α = 0.5, from log M⋆/M⊙ = 8 to log M⋆/M⊙ = 10.5. The UDF sample supports a redshift evolution j̃⋆ ∝(1+z)a, with a = −0.27−0.56+0.42 which is 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 logj|M⋆ ∝ 0.65−0.08+0.06 × log(Vmax/σ), where σ is the velocity dispersion at 2Re. In TNG50, SFGs also form a j̃⋆−M⋆−(V/σ) plane, but it correlates more with galaxy size than with morphological parameters. Our results suggest that SFGs might experience a dynamical transformation, and lose their sAM, before their morphological transformation to becoming passive via either merging or secular evolution.