Does Jesus's soul exist before his incarnation? I am referring to clause III in "The Anathematisms of the Emperor Justinian Against Origen":


  If anyone says or thinks that the soul of the Lord pre-existed and was
  united with God the Word before the Incarnation and Conception of the
  Virgin, let him be anathema.


This seems inconsistent with an important pillar of orthodox Christianity (not to be confused with eastern orthodoxy) doctrines: the doctrine of Trinity, which states that the Father, the Son and the Holy Spirit always exist.


  All three divine Persons—Father, Son and Holy Spirit—share the one
  being of God. The Trinity doctrine explains that Jesus was not created
  sometime prior to his incarnation, but existed eternally as God.


Obviously these two can't be both right, so, how can "The Anathematisms of the Emperor Justinian Against Origen" and the Trinity doctrine be reconciled from orthodox Christianity point of view? Or the view expressed in "he Anathematisms of the Emperor Justinian Against Origen" is never a part of Christianity teaching?
This is one of the popular misconception of trinity and incarnation.

Jesus as Logos (The Word) is divine. He existed in that form for eternity in the Trinity. But the humanity of Christ did NOT exist before incarnation. Humanity of Christ consists of his human soul and body. Humans are made up of soul and body, so when Christ became human, ie., when he took human flesh (physical) and soul (spiritual) form, he raised it to the level of his divinity. This raising was completed to the fullest extent in his resurrection thru his glorified humanity (body and soul).


  "At the very instant (of incarnation) that there was flesh, it was the flesh of the Word of God, it was flesh animated with a rational and intellectual soul." - Damascene (De Fide Orth. iii)


Note that God the Father or God the Holy Spirit do NOT have a soul.