Where did you get the word "inherit" from? Which translation? The six versions I've looked at all have this: 2Ki 2:9 It happened, when they had gone over, that Elijah said to Elisha, Ask what I shall do for you, before I am taken from you. Elisha said, please let a double portion of your spirit be on me.
The word "yarash" is usually translated as "inherit" and that doesn't appear anywhere in the verse.
It makes more sense that he actually wrote the letter and didn't go to heaven...
Only because of your other presumptions. If Elijah was still on this earth, where was he? If he was close enough to easily arrange the delivery of a letter, then why did he not just come in person? If he was far away, then how did he arrange for it to be delivered? No Fed Ex available back then. Not even the Roman postal system. Why didn't he come and give his message in person? It sure would have been easier on Jeremiah if he could have sent his prophecies to Jerusalem by slow camel. I'm sure Jonah would have preferred to write a letter rather than going to Ninevah in person.
Beats me. But the fact remains that a Jeromeh was reading a letter from Elijah years after he supposedly went to heaven. Scripture doesn't say how he got it though.
Enoch dies but we don't know what God did with him,
That contradicts the passage from Hebrews I cited. It says that Enoch "was taken up so that he should not see death". If you believe the whole of the Christian scriptures to be inspired, you need to reconcile what Jesus said with what the author of Hebrews said.
Heb 9:27 And as it is appointed to men once to die, but after this the judgment,
Enoch had to have died a physical death. Even Christ had to endure a physical death. Maybe Paul was just saying that God took him away somewhere to save him from being killed by someone or something...who knows? The scripture is silent again.
An online RSV. Typically, I've found it to be an accurate translation. I use this particular online reference because it has good search capabilities. In this case, I did not check it against other translations. I looked up a Jewish translation and it also renders the passage "let a double portion of thy spirit be upon me". I cede the point on "inherit" to you. However, I continue to disagree about the fate of Elijah.