II. Each Person in the Trinity took part in our Redemption
The fact, therefore, that, with the co-operation of the inseparable Godhead still perfect, certain things are performed by the Father, certain by the Son, and certain by the Holy Spirit, in particular belongs to the ordering of our Redemption and the method of our salvation. For if man, made after the image and likeness of God, had retained the dignity of his own nature, and had not been deceived by the devil's wiles into transgressing through lust the law laid down for him, the Creator of the world would not have become a Creature, the Eternal would not have entered the sphere of time, nor God the Son, Who is equal with God the Father, have assumed the form of a slave and the likeness of sinful flesh.
But because “by the devil's malice death entered into the world,” and captive humanity could not otherwise be set free without His undertaking our cause, Who without loss of His majesty should both become true Man, and alone have no taint of sin, the mercy of the Trinity divided for Itself the work of our restoration in such a way that the Father should be propitiated, the Son should propitiate, and the Holy Ghost enkindle. For it was necessary that those who are to be saved should also do something on their part, and by the turning of their hearts to the Redeemer should quit the dominion of the enemy, even as the Apostle says, “God sent the Spirit of His Son into our hearts, crying Abba, Father,” “And where the Spirit of the Lord is, there is liberty,” and “no one can call Jesus Lord except in the Holy Spirit.”
Source: Sermons (New Advent)