The letter proves that Elijah was alive after king Jehoram of Israel killed his own brothers, and that happened five years after king Joram of Judah began to reign, which is exactly when Elijah was taken up in the whirlwind.
Bottom line, Elijah survived the whirlwind. Unless you suppose that Elijah sent that letter from the third heaven down to earth, but I'm not sure the post man travels out that way.
The whirlwind was not a tornado or some natural disaster that he would survive -
it was how Elijah was transported up into heaven
reread my post -IF Elijah was returned to earth we would have scripture that says that -
Read the entire chapter 2
2King2
2
When the Lord was about to take Elijah up to heaven in a whirlwind, Elijah and Elisha were on their way from Gilgal.
3 The company of the prophets at Bethel came out to Elisha and asked,
“Do you know that the Lord is going to take your master from you today?”
“Yes, I know,” Elisha replied, “so be quiet.”
“Let me inherit a double portion of your spirit,” Elisha replied.
10 “You have asked a difficult thing,”
Elijah said, “yet if you see me when I am taken from you, it will be yours—otherwise, it will not.”
11
As they were walking along and talking together,
suddenly a chariot of fire and horses of fire appeared and separated the two of them,
and Elijah went up to heaven in a whirlwind.
12 Elisha saw this and cried out, “My father! My father!
The chariots and horsemen of Israel!” And Elisha saw him no more. Then he took hold of his garment and tore it in two.
Elijah was expecting to be taken
There is no scripture evidence that Elijah ever returned to the earth - None
to say the letter is proof is nothing more that supposition, -the most likely thing is that Elijah wrote the prophecy down and sent it in a letter prior to this event of Elijah being taken , that was either somehow delayed in delivering , sent to the wrong person , was misplaced