Well, here's a third interpretation, one I believe to be in harmony with other passages in the New Testament. First what I believe to be the correct translation of the sentence:
The last Adam became the life-giving Spirit.
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"Ahhh...," you say, "but 'spirit' does not have the article." True, but irrelevant. I did a search for "spirit" in my Online Bible program, and in the first four results, the word referred to the Holy Spirit, but the word has no article. Here are the first four verses in the New Testament that contain the word "spirit":
Matthew 1:18 Now the birth of Jesus Christ took place in this way. When his mother Mary had been betrothed to Joseph, before they came together she was found to be with child from the Holy Spirit.
Matthew 1:20 But as he considered these things, behold, an angel of the Lord appeared to him in a dream, saying, “Joseph, son of David, do not fear to take Mary as your wife, for that which is conceived in her is from the Holy Spirit.
Matthew 3:11 “I baptize you with water for repentance, but he who is coming after me is mightier than I, whose sandals I am not worthy to carry. He will baptize you with the Holy Spirit and with fire.
Matthew 3:16 And when Jesus was baptized, immediately he went up from the water, and behold, the heavens were opened to him, and he saw the Spirit of God descending like a dove and coming to rest on him.
In none of these verses is there an article modifying "Spirit" or "Holy Spirit." And I don't think anyone would want to translate "the Holy Spirit" in the first three as "a holy spirit." Nor would they want to say that Jesus saw "a spirit of God" descending on Him.
So what would it mean for Jesus to become THE life-giving Spirit, that is, the Holy Spirit? And where else does the New Testament indicate such?
The meaning is that Jesus, while He walked this earth was fully human. But when He died and God raised Him to life again, He became the Holy Spirit that indwells his disciples.
Where else does the New Testament indicate this?
But their minds were hardened. For to this day, when they [the Jews] read the old covenant, that same veil remains unlifted, because only through Christ is it taken away. Yes, to this day whenever Moses is read a veil lies over their hearts. But when one turns to the Lord [Jesus], the veil is removed. Now the Lord [Jesus] is the Spirit, and where the Spirit of the Lord [Jesus] is, there is freedom. And we all, with unveiled face, beholding the glory of the Lord [Jesus], are being transformed into the same image from one degree of glory to another. For this comes from the Lord [Jesus] who is the Spirit.(2 Cor 3:14-16 ESV, bracketed explanatory words mine)
Twice in this passage the Lord Jesus is declared to be THE Spirit (the article IS present in this passage), and that would be after He was raised from the dead. Of course, if one has been convinced that the Holy Spirit is a third divine Person different from the Father and the Son, this will make no sense, and he must explain it some other way. But if we can accept that the Holy Spirit is the extension of the Persons of the Father and of the Son, it makes perfect sense. That's why Jesus said if He should not go away, the Spirit would not come to his disciples:
Nevertheless I tell you the truth: it is to your advantage that I go away, for if I should not go away, the Advocate would not come to you; but if I should go, I will send him to you. (John 16:7)
There is only one future tense in this verse, and that is the verb in "I will send him to you." The rest of the verbs are in the subjunctive mode. Thus He seems to say that He must go away, die, and be raised or the Holy Spirit, the Advocate could not come. Why couldn't the Holy Spirit, the Advocate come to them while Jesus was still with them? Because the Lord Jesus IS the Spirit as I showed from the verses quoted above. While He lived as a total human being on earth, his spirit was confined to his body. But when He was raised, He became the Spirit again. Jesus promised that He and the Father would love anyone who kept his word, and that He and the Father could come to him and make their home with him (John 14:23). How would they do that? By extending their persons into Jesus' disciples. And that extension of their Persons IS the Holy Spirit.
Another support I have for my understanding that Jesus IS the Spirit, the Advocate, is that He is called "the Advocate" in 1 John 2:1.