。
Has she finished reading that book?
Literal
[topic-は] already that book [object-を] read-finish-did [question-か]?
読み終える is a compound verb — 読む ('read') + 終える ('finish [transitive]') — yielding 'finish reading.' The auxiliary ~終える marks the completion of an action and pairs with all sorts of activity verbs: 食べ終える ('finish eating'), 書き終える ('finish writing'), 見終える ('finish watching'). Note 終える is the transitive twin of 終わる ('come to an end, intransitive'); both can serve as the auxiliary, with 終わる the slightly more common everyday choice. もう in a question reads as 'yet' (matching the question-direction expectation), not 'already.'