Here’s my point from what i’ve gathered: It wasn’t specifically stated but i think the brain fog caused by the tumor was affecting his memory but i’m assuming his memory was still able to function, it was just that his memory recall is too slow than those without a tumor.
If you go back to the panel where he got diagnosed he said his first instinct was to leave Hyeonji and from that point he could’ve already written a letter its not like he’d immediately forget his diagnosis and he was even still able to go back to the US cause he still knows the reason why he has to go back (Tumor and treatment stuff)
+ He didn't have to make a very detailed letter anyway he could've just said that he had a tumor and is going back to the US to be treated and an apology for suddenly leaving that’s it.

Man the backstory of the dad was really sad. I really branded him as a scumbag ever since Mr. Kwon mentioned him and now i regret judging. If i were to put myself in Mr. Kwon’s shoes tho i’d probably be mad but for a different reason now after explaining his side cause he could’ve at-least left a letter like i know my mom would be worried but its better that she knew so that he wouldn’t have broken her heart like that and cause a misunderstanding. I believe Mr. Kwon has every right to decide if he’s willing to forgive his father but i hope they atleast reach a point where they’ve come to terms with it