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 Sersic 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 Sersic 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.
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