As a Muslim, who was a Catholic, the argument the Muslim brother is attempting, unsuccessfully, to use, is bunk.
From within the doctrine taught by mainstream Christianity, that of vicarious/substitutionary atonement: Jesus did not die except in the flesh, as his spirit is eternal (the uncreated Logos) and is of the same essence (ousia) as that of God (this is how substitutionary atonement works: because God is infinite, and Jesus was God, so Jesus’ death/suffering could be infinite, and therefore able to atone for all of the finite sins of humanity, as a finite death could not) but instead descended in to Hell, then rose again, and then ascended to Heaven.
Such as this: according to doctrine, Jesus was 100% God and 100% Man. The entirety of his human nature could, and did, die, without affecting his Godly nature, whereas his Godly nature was responsible for the workings of substitionary atonement.
Not to mention that it is obvious from the Bible that God was still in Heaven while Jesus was on Earth (cf. next paragraph), so that even if Jesus died fully and completely, God would not be dying. Many people less knowledgeable in the theology of multiple religions will use such pedantic and narrow arguments, cherry-picking parts of each Holy Book in order to try to bolster their own position (a “straw-man” argument) in my experience.
There are many better arguments against the hypostases/ousia Trinitarian theory, some being that Jesus prayed to God many times (cf. the Agony in the Garden), and said words to the effect of, “I do not know the time appointed, nor do the angels in Heaven: that knowledge is of the Father alone”, or the famous last words of Jesus upon the Crucifix, from off the top of my head.
The doctrine of substitutionary atonement leads to antinomianism: no matter how many creeds reject it (antinomianism), the only logical conclusion of “salvation by faith alone” is the complete abrogation of all mortal and divine law.
Essentially, the concept of the Trinity is not a rational one: it is a “divine mystery”, and requires faith, as, according to doctrine, it is too large, alien, divine, et cetera for a human mind to be able to comprehend: even within Christianity there are more interpretations of the Trinity (and grace as a whole, resistible, efficacious, etc.) than verses in the Gospel according to John.