Definition (house style)
“Life-giving Spirit” is the expression Paul uses in 1 Cor. 15:45 for the exalted Christ after the resurrection: “The last Adam became a life-giving spirit” (πνεῦμα ζῳοποιοῦν). This binds the risen Christ to the Holy Spirit in a theologically complex way: not that Christ and the Spirit are the same Person, but that the glorified Christ works so completely through the Spirit that “the Spirit of Christ” (Rom. 8:9) and “Christ in you” (Rom. 8:10) become functionally coextensive. 2 Cor. 3:17 adds: “The Lord is the Spirit.”
On apokatastasis.wiki this concept is especially significant through Nee/Lee: the risen Christ has placed all seven redemptive-historical elements (divine nature, incarnation, human life, death, resurrection, ascension, enthronement) into the all-inclusive Spirit. Whoever receives the Spirit receives the complete, all-inclusive Christ.
Usage per author
Nee/Lee
Lee describes the pneumatological-christological transition after the resurrection as a radical enrichment of the Spirit:
“The Holy Spirit after the Lord’s ascension is no longer the same as the Spirit of God in Old Testament times. The Spirit of God in the Old Testament had only one element — the divine nature of God. Today, however, under the New Testament economy, all seven elements of Christ have been placed into the Spirit, and as such this all-inclusive Spirit has come into us.”
[Lee, The Economy of God, ch. 1]
Directly citing 1 Cor. 15:45 and 2 Cor. 3:17:
“The last Adam became a life-giving spirit (1 Cor. 15:45). Now the Lord is the Spirit (2 Cor. 3:17).”
[Lee, The Economy of God, ch. 1 and 2]
In Lee, “life-giving Spirit” is the comprehensive christological synthesis: everything Christ accomplished in his redemptive-historical acts — from incarnation to enthronement — is now actively present in the Spirit indwelling believers. The Spirit is not a partial outpouring but the complete Christ in pneumatic form.