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 Sydney-AAO Multi-object Integral field Galaxy Survey. We find that j, measured within one effective radius, monotonically increases with M * and that, for M * > 109.5 M⊙, the scatter in this relation strongly correlates with optical morphology (i.e. visual classification and Sérsic 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 3. Indeed, the stellar spin parameter (quantified via λ R ) correlates strongly with Sérsic 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.