If the Holy Spirit is the Spirit of the Father then does it follow that He is technically the Father?

According to Bible Trinitarians, let's assume that there is Samuel the prophet(before he died) and Samuel the spirit(after he died), so after the medium at Endor called his spirit from the dead, he was still Samuel the prophet technically because he still prophesied onto Saul that he would die the following day. Can this analogy be applied to demystify the divine nature of the Holy Spirit as being the Father? That is because I am So Few Against So Many in the flesh but also the same person in the spirit for even that medium must have acquired the name of Samuel from Saul, I am still the same person but with a different essence? So the Spirit is still the Father but in a different essence? Does this explain why the Father is not mentioned in the sermon about the unforgivable sin? Because he is literally the Holy Spirit? There is Jesus who was dead on the cross and Jesus who descended into the heart of the earth in spirit form, both were still Jesus.