If you unsealed the letter at any point before delivering it, you will find it impossible to persuade Kha'Raji to accept Walks-Through-Shadow's offer.
If Kha'Raji is dead, your reward will be only 800 gold, while if you successfully persuade him to come to Firewatch, it will be 2,500 gold (and +5 Twin Lamps reputation).
The following Journal ID and Index codes can be used with the Journalconsole command to manually update the quest to a certain point.
Letter for Kha'Raji (PC_m0_FW_LetKha)
Index
Finishes Quest
Journal Entry
10
Walks-Through-Shadow, a professor at the College of Firewatch in Morrowind, asked me to deliver a letter to Kha'Raji, an academic who resides in the Kingdom of Anvil in Cyrodiil. He promised to pay me well if I deliver the letter and return with Kha'Raji's answer. I was told that Titus Corilex could take me to Anvil on an East Empire Company ship docked in Old Ebonheart.
20
I spoke with Elisanne, Kha'Raji's wife, at their home in the Wayfarer Building in Anvil's Marina. Elisanne informed me that Kha'Raji recently traveled from Anvil to Brina Cross to pick up some books from Karlorume's bookstore.
30
Kha'Raji read the letter I delivered. He said he would need to head back home to think about its contents and discuss them with Elisanne before answering me, and asked me to meet him back there.
40
Kha'Raji told me that he must decline the letter's offer. He asked me to pass along his apologies to Walks-Through-Shadow.
50
I persuaded Kha'Raji to accept the letter's offer after revealing my connection to the Twin Lamps. Kha'Raji told me to let Walks-Through-Shadow know of his acceptance. He said he would head to the College of Firewatch in Morrowind soon.
60
Kha'Raji is dead.
100
Finishes quest
Walks-Through-Shadow paid me for delivering the letter to Kha'Raji.
110
Finishes quest
Walks-Through-Shadow paid me for delivering the letter to Kha'Raji. He also gave me a little bonus for persuading Kha'Raji to accept his offer.
120
Finishes quest
Walks-Through-Shadow was saddened to hear that Kha'Raji is dead, but reimbursed me for my travel costs regardless.