To answer your question, it is absolutely necessary to treat theological and Christological issue: a) what is the reality of God, His Spirit and His Logos-Son and b) how Jesus, the Logos-Son incarnate in history, is related to the Holy Spirit after the Incarnation? Below I shall address those issues and try eventually to find the solution to your question also.
The New Testament, and the Bible in general, does not have a very strict terminology with regard of "soul" and "spirit" and sometimes they are used interchangeably as standing for the created reasonable soul of human being, through presence of which he moves, desires and, which is even more important, thinks. However, the New Testament also speaks of the uncreated Spirit of God through whom one can receive the "new birth" (John 3:3). Humans, qua created and limited, have the presence of the Spirit in a dynamically apportioned way, for it is impossible for finite beings to possess the infinite divine Spirit in His fullness, for only God can claim this. Now, Spirit possesses all what belongs to God, for He "knows even the depths of God" (1 Cor. 2:10), and in this way the Spirit is equal to God, for epistemological equality in the invisible and purely spiritual realm amounts to ontological equality; and by the same token also the Son is equal to the Father and the Spirit, for the Spirit receives everything from the Son, who has everything of the Father (John 16:15). This fullness of the Spirit and the Son with all infinite riches of God in actual infinity is not temporal and processual/gradational, but eternal and instantaneous, and this common fullness with the same infinite reality of the Three - the Father, the Spirit and the Son - has been there even before the world was created, in all eternity, and such a volitional act as creation of the universe can in not even a tiny bit change anything in the changeless trinitarian relationship of love in the Godhead, for God is eternal changeless love of divine Persons, and that is the meaning of the verse "God is love" (1 John 4:8). In fact, a Mono-Personal Absolute cannot be the God of love, for before creation of the world He would love only Himself, and be thus the Absolute lonely Egoist; but the Christian God, the eternal Father loved eternally His co-eternal Son even before He created the world through Him (John 17:24).
This said, we can firmly hold in mind's gaze: Trinitarian Persons are indivisible. To give just an analogy: can you disentangle water from wetness? Not, of course. Infinitely more so, you cannot disentangle the Persons of the Trinity from each other, although neither are they mixed, as to lose the Personal distinctions, for the Father is not the Son and the Son is not the Holy Spirit, even if the reality of the Three is one and identical.
Now, Christology: who is Christ? He is the Logos-Son Incarnate, that is to say, Logos-Son having adopted the human nature, or human created body invested with intelligent created soul. Thus, Logos, who always is with the Father and the Spirit inseparably, has adopted the human ensouled body, which is another wording for "human nature". At the death on the Calvary Jesus gave His human created soul to the "hands of the Father", as the dying man does, but this human created soul does not perish on the hands of God, for how can anything die received by the vivifying "hand" of the Father; of course this "hand" is not a physical hand but a metaphor for His Spirit (in fact, the Spirit of God is equated with the "finger of God" in the parallel passages of Matthew 12:28, Luke 11:20), and this is the meaning of 1 Peter 3:18, that His body died, but His soul was vivified by Spirit, that is to say, by the vivifying "hand of the Father", and by the Logos-Son also, who, as God, has authority and power to vivify, for Logos, qua God, could not die, for it is ontologically impossible for God's eternal Logos to die; but we justly say, that Logos in a certain sense, suffered and died on the Cross, for Logos' human body became, by adoption, by His volition, eternal aspect of His Personality, so that after the Incarnation we can think of the invisible divine Person of Logos only together with His human nature and human body, and since His body really died, we somehow say that "God's Logos died", "God's co-eternal Son died". But of course, when we say this, we imply that His body died, that is to say, the Logos' created soul was separated from His created body; as, for instance, when Paul passionately desires for death, he in fact desires that his soul is separated from the physical body and joining eternally Christ (Phil 1:23) (for it is impossible to suppose that he longs for total annihilation in this manner, for annihilation and complete "switching off" of consciousness before the general resurrection simply cannot be more desirable for Paul than being with his beloved Christian community on earth, but being, after physical death, with Christ with a greater intensity of graceful interaction - that is truly more desirable even than being with the beloved brethren-Christians on earth). Thus, neither Father, nor Holy Spirit never ever have left the Logos, either before the Incarnation, or after the Incarnation (when the Incarnate Logos, the Logos who became also son of a man, was called Jesus Christ and eternally so henceforth), or on the Calvary, when He in His human nature was undergoing unspeakable sufferings and eventually also underwent death - the separation of His, Uncreated Logos' created soul from His, Uncreated Logos' created body.
Apologizes for the length of the answer, but it is difficult to make shorter such a breathtakingly difficult issues.