ADDED: I'm sorry to have gone off on the wrong trail in response to the question raised here. Certainly Philip Hall's influence on other group theorists was not limited to his formally published work, though I suspect the informal stuff left out of his collected works might be covered indirectly through the papers he inspired other people to write. Though not many people directly involved in that era remain, it would for example be interesting to know what John Thompson's recollections are.
Perhaps it may inspire some finite group theorists to suggest better answers if I quote more precisely the "theorem of Philip Hall" which Gorenstein revisited from the viewpoint of the 1963 Feit-Thompson paper:
$P$ is a
$p$-group with no noncyclic characteristic abelian subgroups, then
$P$ is the central product of subgroups
$P_1$ is extra-special and either
$P_2$ is cyclic or
$P_2$ is dihedral, generalized quaternion, or semi-dihedral."