The clue to the Operational Structure of the Life and Being of the One God and Father of us all is in the 'Names' of each of the Three Persons Who together constitute the Life and Being of what is the One Communal Life of the Divinity.
The eternal act of the Father's self-knowledge and understanding of Himself is an eternal act of generation within His Personage of the total Self-Image of Who and What He IS, and as the Father is a 'Person', so too is His Self-Image a 'Person' - a 'Person' Who is 'Son' - because He is the eternally 'generated' Living Son-Image of all that His Father IS. He is all of what the Father is - except being the Father. They exist, intrinsically one together, such that one does not exist without the other. And so, the Godhead is unequivocally, not one, but two, identical Communal Persons, such that the Son can eternally say, "Who sees Me, sees the Father, and from now on you have seen Him. (John 14:7-11) All that the Father does, so do I. As the Father gives life to whomever He chooses, so do I. My will is in total accord with the Will of My Father and so I do always what pleases Him. (John 8:29) The Father and I are One such that all that the Father is, so too, I AM. (John 8:58) All that He is, and has, are Mine, and that is why the Spirit generated from both of Our Hearts is the Same One Holy Spirit of Whom I can say, "Whatever the Holy Spirit tells you will be taken from all which is Mine." (John 16:13-15)
So, when the Spirit acts, His actions are actions of the Hearts of the Father and the Son together, such that it can be clearly understood that, "Where one acts, all act" - the Father, the Son, and their Holy Spirit - 'The Holy Trinity'.
To repeat: The Son is generated eternally of the Father, and the One Spirit of their hearts is eternally generated of both the Father and the Son. And so it is, that the Father's will is the Communal action of all Three. "Where one acts, all act." The classic example of this is when: in accordance with the Father's will, the Son was incarnated in the Immaculate Virgin's womb by the overshadowing power of the Divinity's Holy Spirit for the purpose of repentant mankind's merciful redemption. (Genesis 3:15; Isaiah 7:14; Luke 1:35; Apoc.12:1-17)
"O, endless love, praise, thanks and adoration be forever Yours, O Wondrous Holy Trinity!"
And the Lord God said: "I will pour out My Spirit on all mankind."
(Joel 2:28; Acts 2:17)
"There are three Who bear witness in Heaven,
the Father, the Son and (their One) Holy Spirit,
and these Three are One."
(1 John 5:7)
See also: Understanding The Holy Trinity