My blog’s domain name has in it the word, “huper“.
“On behalf of” is the phrase used over and over in the NT to mark the “proxy-exchange” taking place there.
The 2 Corinthians 5:15 testimony marks the high point of it:
“…and he died [huper] on-behalf-of all
so that the ones living would live no more for themselves,
but for him who died and was raised [huper] on-behalf-of them.”
Over and over again, huper is used  when dealing with the most critical matters done for us through The Son. It is the promethean Greek preposition that carries the full scope of “grace”.
(See samples, all as taken from the RSV/IntGE):
“…while yet sinners, Christ died on-our-behalf.” (Rom. 5:6ff.);
“…made to be sin on-our-behalf…“ (2 Cor. 5:21);
“… a curse on-our-behalf …” (Gal. 3:13);
“…so that by the grace of God he might taste death on-behalf-of everyone.” (Hebrews 2:9)
But , correspondingly, the same expression is called on to note “the Kingdom life-pattern” designed for the People of God—”on-behalf-of” one another, on-behalf-of the LORD and on-behalf-of his enterprise.
“…worthy to suffer shame on-behalf-of His Name”. (Acts 5:41);
“…the members of the Body to have the same care on-behalf-of each other.” (1 Cor. 12:25);
“…to fill up in my own flesh the afflictions lacking of Christ on-behalf-of the Body.” (Col. 1:24)
With the genitive, 134 times, mostly with regard to God’s activity; op. cit., J.B.Smith’ss Greek-English Concordance, 5128a.