The correct view is that she is not required to perform Zuhr.
His statement, “If its time ends before the opening takbir, they pray Zuhr; otherwise, they pray Jumu‘ah”: “If its time ends” means: if the time for Jumu‘ah ends.
“Before the opening takbir” means before the takbir for entering the prayer. In that case, they pray Zuhr, because the time has elapsed. A prayer time is only considered to have been caught by performing the opening takbir; thus, whoever has not performed the opening takbir before the time ends has missed the time. What the author, may Allah have mercy on him, has followed here is based on the view that catching the prayer time is attained by the opening takbir.
The correct view is that it is not attained except by completing one rak‘ah, due to the Prophet’s statement, peace and blessings be upon him: “Whoever catches one rak‘ah of the prayer has caught the prayer.” (1)
Accordingly, we say: if its time ends before they have caught one rak‘ah, they pray Zuhr.
Issue: If only enough time remains for the obligatory portion of the sermon, what should they pray?
The answer is: they pray Zuhr, because it is not possible to establish Jumu‘ah, as Jumu‘ah must be preceded by two sermons. Thus, there must remain within the time of Jumu‘ah enough time for the obligatory portion of both sermons, as well as enough time for the opening takbir according to the author’s view, or for one rak‘ah according to the view we have deemed preponderant.
If someone were to ask: Can the time for Jumu‘ah prayer end for all the people?