  We investigate the relationship between stellar and gas specific angular
momentum $j$, stellar mass $M_{*}$ and optical morphology for a sample of 488
galaxies extracted from the SAMI Galaxy Survey. We find that $j$, measured
within one effective radius, monotonically increases with $M_{*}$ and that, for
$M_{*}>$10$^{9.5}$ M$_{\odot}$, the scatter in this relation strongly
correlates with optical morphology (i.e., visual classification and S\'ersic
index). These findings confirm that massive galaxies of all types lie on a
plane relating mass, angular momentum and stellar light distribution, and
suggest that the large-scale morphology of a galaxy is regulated by its mass
and dynamical state. We show that the significant scatter in the $M_{*}-j$
relation is accounted for by the fact that, at fixed stellar mass, the
contribution of ordered motions to the dynamical support of galaxies varies by
at least a factor of three. Indeed, the stellar spin parameter (quantified via
$\lambda_R$) correlates strongly with S\'ersic and concentration indices. This
correlation is particularly strong once slow-rotators are removed from the
sample, showing that late-type galaxies and early-type fast rotators form a
continuous class of objects in terms of their kinematic properties.
