7 Nevertheless I tell you the truth. It is to your advantage that I go away; for if I do not go away, the Helper will not come to you; but if I depart, I will send Him to you.
8 And when He has come, He will convict the world of sin, and of righteousness, and of judgment:
9 of sin, because they do not believe in Me;
10 of righteousness, because I go to My Father and you see Me no more;
11 of judgment, because the ruler of this world is judged.
go away (v. 7) — two-fold fulfillment: 1) the cross. It was expedient that He should suffer and die, and 2) His ascension, so the Spirit would come which could not happen until after the atonement (the cross again).
The omnipresence of the Spirit (v. 7) is better than the presence of the Son in His localized humiliation of the flesh.
The proof of verse 7 is that the disciples accomplished far more in the power of the Spirit at and after Pentecost than they did in Christ's presence when He was on earth.
convict (v.8) = to prove wrong, conviction by demonstration, by an unanswerable argument — pronounce judgment with no confession of feeling of guilt by the one judged. It's an objective condemnation, not a subjective realization of condemnation.
The Spirit's presence (v. 9) demonstrates that the world rejected Christ. But this He spoke concerning the Spirit, whom those believing in Him would receive; for the Holy Spirit was not yet given, because Jesus was not yet glorified (John 7:39).
That Christ was received by the Father (v. 10) proves His righteousness. That the Spirit is here proves that Christ was received.
The Spirit's presence (v. 11) demonstrates the coming judgment because Satan's judgment has already been proclaimed. (Hebrews 2:14)
The Spirit ought not to be here. The Father sent the Son, but the world rejected Him. The Spirit is here in place of the Son, and His presence proves the world's guilt.
The Spirit is the advocate — In judicial terms, the prosecuting attorney (advocate). He proves guilt before the court.
These verses don't refer to what the Spirit does on earth, but show the consequences of His presence.