I’m looking for proof that the Nevi’im and Ketuvim in the Septuagint were translated by christians, and not by jews.

You see, I got into a conversation with a christian missionary, and he made a video about the blatant difference between jewish and christian bibles in Psalm 22:17 (22:16 in christian bibles). In the video, he correctly points out that the origin of the difference is the Septuagint. He then claims that all of it was translated by jews. I commented, and said that the Nevi’im and Ketuvim were translated by christians. He commented, and said that even the Jewish Encyclopedia says that the “Law, Prophets, and the rest of the books” were translated as current as 132 BC. He linked to the JE article, so I looked at it. Turns out that the saying above is just what the grandson of Ben Sirach said in the opening to his greek translation of his grandfather’s book. Now, could you help me with this affair?