"You should remember posting for me" is not grammatical.
Sorry, I disagree. An action like posting doesn't need an explicit object to make a sentence grammatical - though I agree there would
be an implicit object, since 'post' isn't intransitive.
"You wash and I'll dry. Can you dry [the dishes] for me?"; "My arm's broken. Can you drive [the car] for me?";
"Can you cook/clean for me?"
B is possible in this way; the others aren't, except perhaps C "to be posting", where again, there would be an implied object. But C is a far less likely sentence, making B the only reasonable answer. "To post" is also possible.