。
She wrote down his words.
Literal
She [topic-は] his [genitive-の] words [object-を] wrote-down.
書き留める is a 複合動詞 from 書く ('write') + 留める ('fix in place, fasten') — 'write so as to fix' = 'write down, jot down.' The auxiliary 留める adds the sense of recording for later reference, distinct from plain 書く ('write'). Common with notes, observations, lectures, conversations.