Chapter — Slater, Manual of Moral Theology
Chapter II. The Minister of Extreme Unction
ONLY a bishop or a priest can validly administer this sacrament, and the only lawful minister is the bishop or priest who has the cure of souls in the place where the sick man dwells, or another priest with his express or at least reasonably presumed leave.
p. ii, 181
In the Latin Church one priest performs all the unctions, but the sacrament is valid if different priests perform the several unctions, as is done in the Greek Church. The organs should not merely be touched with the holy oil, but anointed, and the Ritual prescribes that this should be done by making the sign of the Cross on the organ with the thumb after dipping it in the oil. Care should be taken not to finish the form before both organs have been anointed when they are double, and the several anointings should be done continuously, as it is probable that all together constitute the sacrament by which grace is not given until the last anointing is finished.
p. ii, 181