So which is it? There was a whole Jewish Septuagint long before the arrival of Christianity, or, the Jewish canon wasn’t fixed until after Christianity arrived (so they knew which books to include in the Septuagint)?
The original Septuagint was of the Five Books of Moses only, and easily predates subsequent unofficial translations of some Prophets and Writings. Where would one find a complete copy of the original Septuagint, whatever it was?
The entire Septuagint was pre-Christian, and the New Testament quotes from it, including Pentateuch, Psalms, Prophets, etc. Philo and Josephus (both Jews, Philo died before Christ was born) held it in great respect.
http://en.wikipedia.org/wiki/Septuagint
http://en.wikipedia.org/wiki/Septuagint_manuscripts
Having entire ancient manuscripts in one’s hands that date near when the original was completed is always a problem. (If one thinks about Homer, one sees this without all the controversies that accompany anything to do with the Bible.) The first complete Hebrew Bible manuscript we have is relatively late, too.