All of the grammar folks out there will recall certain rules about Subject-Verb agreement, and placement of "Ly" adverbs.
A condensed version is that "Ly" adverbs are placed between subject/verb in English sentences to describe actions the subject itself is taking via the verb used, and noun-descriptively when placed after a subject but not followed by a verb.
In other words, "posthumously" is out of place, here.
Correct grammar:
“…would let President Joe Biden promote Grant posthumously”.
👉 RealSGAnon