It is common knowledge that the apostle knew by heart the entire text of the Hebrew Scriptures. He also was able to cite another version at will: the Greek version of the Bible known as the Septuagint. This is the version he almost always quote in his letters to Greek-speaking Christians.
Thus: when he quoted from the Scriptures, he didn’t have to look it up.
Just ran across this tradition concerning the rabbi Shammai, the important theologian who lived in the first century BC, that is, a couple of generations before Paul. He affirmed that in effect he owned two copies of the Bible:
There was the incident of a certain gentile who came before Shammai. He said to him, “How many Torahs do you have?” [Shammai] said to him, “Two, one in writing, one memorized.” [b. Shabbat 31A, Babylonian Talmud, Neusner edition, 2:127]
Two copies of the Bible, true for Shammai, true for Paul. How true is this for us?
“Paul had the Bible memorized!” by Gary S. Shogren, Seminario ESEPA, San José, Costa Rica