。
She acknowledged that he was the murderer.
Literal
She [topic-は] him [object-を] murderer [as-だと] acknowledged.
認める covers a cluster of meanings — 'to recognize, acknowledge, admit, accept' — and the Xを Yだと認める pattern means 'to acknowledge that X is Y' or 'to recognize X as Y.' The だ before と is the copula carrying the predicate inside the quote. 殺人犯 ('homicide perpetrator') is the formal/legal term for murderer; compare the blunter, colloquial 人殺し. The だ here adds emphasis — without it (彼を殺人犯と認めた) the sentence would sound more like a categorical declaration; with it, the predicate feels asserted rather than just labeled.