  Let $G=\mathbf{G}(\mathbb{R})$ be the group of real points of a quasi-split
connected reductive algebraic group defined over $\mathbb{R}$. Assume
furthermore that $G$ is a classical group (symplectic, special orthogonal or
unitary). We show that the packets of irreducible unitary cohomological
representations defined by Adams and Johnson in 1987 coincide with the ones
defined recently by J. Arthur in his work on the classification of the discrete
automorphic spectrum of classical groups (C.-P. Mok for unitary groups). For
this, we compute the endoscopic transfer of the stable distributions on $G$
supported by these packets to twisted $\mathbf{GL}_N$ in terms of standard
modules and show that it coincides with the twisted trace prescribed by Arthur.
