I note that become was accepted as a translation of gheS in another sentence, which makes wonder if this sentence can also be translated simply as Who will become chancellor? or Who became chancellor?
In English, "assume the duties" can imply either taking on the duties of another person temporarily without necessarily succeeding to the position, or alternatively taking over the role completely. Does gheS work the same way?
I don't think we have any evidence regarding your question. I will simply point out that gheS is defined as assume duties of, take on responsibilities of. It's not necessarily about the title; it's about what you're doing.
So to me the more important question is this. Suppose you're the High Administrator (loHwI''a') of your planet and I'm your assistant (boQ). But you're lazy. The economy is falling apart, and you don't care. So I step in and start to do all the work in your name. Is it true that loHwI''a' vIgheS? My gut instinct says no; I feel like gheS is a recognized change of responsibilities. But that's not evidence.
I guess that from a linguists point of view you are right. As a student who saw the tempting short "became" two or three records ahead shown as a valid alternate fact - eh solution - after the tedious typing of "assumed the duties of" I happily used the shorter solution(i.e. "became") when duties were to be assumed. And was not honored for me being smart :-( Maybe it just would be nicer / less confusing if "became" would not be shown as a "another solution" at all?