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If we follow the chronology based on the order the events as presented in 2 Kings and 2 Chronicles,
1. Jehoram is anointed king of Judah (2 Kings 1:17), ruling with his father, Jehoshaphat, for the final 5 or 6 years of his father’s reign.
2. Elijah is translated to heaven (2 Kings 2:1–18).
3. Jehoshaphat, advised by Elisha, teams with the king of Israel in a fight against Moab (2 Kings 3).
4. Jehoshaphat dies, leaving Jehoram to rule alone (2 Chronicles 21:1).
5. Jehoram murders all his brothers (2 Chronicles 21:4) and builds idolatrous high places in Judah (verse 11).
6. Jehoram receives a letter from Elijah that details his judgment (2 Chronicles 21:12–15).
So Elijah was taken up to the skies, the first heaven, and then brought back down again. He did not remain in heaven for all his life, and he never reached the 3rd heaven, where God is sitting.
John 3:13 made it clear "And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven."
1. Jehoram is anointed king of Judah (2 Kings 1:17), ruling with his father, Jehoshaphat, for the final 5 or 6 years of his father’s reign.
2. Elijah is translated to heaven (2 Kings 2:1–18).
3. Jehoshaphat, advised by Elisha, teams with the king of Israel in a fight against Moab (2 Kings 3).
4. Jehoshaphat dies, leaving Jehoram to rule alone (2 Chronicles 21:1).
5. Jehoram murders all his brothers (2 Chronicles 21:4) and builds idolatrous high places in Judah (verse 11).
6. Jehoram receives a letter from Elijah that details his judgment (2 Chronicles 21:12–15).
So Elijah was taken up to the skies, the first heaven, and then brought back down again. He did not remain in heaven for all his life, and he never reached the 3rd heaven, where God is sitting.
John 3:13 made it clear "And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven."
Elijah was not translated until some time during the reign of Jehoram son of Ahab. Jehoram son of Ahab reigned in Israel from about 852 to 841 b.c. Jehoram son of Jehoshaphat reigned in Judah from 848 to 841 b.c. Therefore, since Elijah was not translated until some time in the reign of Jehoram of Israel, it is perfectly reasonable that he could have sent this letter to Jehoram of Judah.
from When Critics Ask: A Popular Handbook on Bible Difficulties (Wheaton, Ill.: Victor Books, 1992). © 2014 Norman Geisler and Thomas Howe.