"sn In 1st century Judaism and in the NT, it was believed that the righteous would be given new, glorified bodies in order to enter heaven (cf. 1 Cor 15:42-49; 2 Cor 5:1-10). This transformation meant that the righteous will share the glory of God. The account of Jesus’ transfiguration here recalls the way Moses shared the Lord’s glory after his visit to the mountain in Exod 34:28-35. So the disciples saw Jesus transfigured, and they were getting a private preview of the great glory that Jesus would have following his exaltation."
But how could Peter, James, and John see Moses? How did the three disciples know that the two were Moses and Elijah? One idea put forward is that they had appeared with Christ in a manner that the three could recognize. Consequently, the disciples correctly identified Moses and Elijah apart from never seeing them previously.
The Scripture is not clear on whether or not we are able to see human souls. Luke 16:19-31 seems to indicate that human souls remain conscious after death and are recognizable to each other. We do need to remember that there are hidden things which God, in His unsearchable wisdom, has chosen not to make known to us (Deuteronomy 29:29).
The point of the Transfiguration is to show the preeminence of Jesus Christ. He does not depend on creation. Christ was speaking with Moses and Elijah on the Mount of Transfiguration in His glory. The appearance of these two men signifies Him being the fulfillment of the Law and the prophets.
God voiced His approval of Jesus Christ from heaven (Matthew 17:5-6). He is the perfect and acceptable sacrifice for sin. The heavenly kingdom was formally instated during the earthly ministry of Christ, but will not be brought to fulfillment until His second coming. He will reign for eternity as the supreme King. Professor Stephen N. Williams gives the following commentary on the Transfiguration:
"There may be reminders or echoes of the scene of transfiguration elsewhere in the NT, of course; the stories of Paul’s own conversion, in the Book of Acts that combine Jesus, light and a voice from heaven; the very rare (NT) word ‘transfigure’ is the one used by Paul when he tells the Corinthians that we ‘are being transformed [‘transfigured’] into his likeness with ever-increasing glory’ (2 Cor. 3:18); the first chapter of Revelation, with its dramatic portrayal of Jesus, has resonances. John’s Gospel is intriguing on this score. It contains no reference to the transfiguration, but it is a Gospel all about ‘glory’ and a voice from heaven thunders that God has glorified his name ‘and will glorify it again’ (12:28). The question about why John does not specifically mention transfiguration belongs to the wider discussion of its relationship to the Synoptics. We must bear in mind that John does not refer directly to the Last Supper either or directly report the actual baptism of Jesus, where the Synoptics do. John can be concerned with the surrounding interpretation of events that he does not report as do the Synoptists."