The Himyarite Kingdom became a Jewish kingdom in what is today Yemen, from around 380 CE at the earliest and continued to be Jewish until around 500 CE with the 530 CE date being the very latest date before they were converted to Christanity. That being said, the Babylonian Talmud was only recently completed c. 500 CE and was still undergoing some minor revisions afterwards. However, the Jerusalem Talmud was completed c. 300 CE.
Having said that, my question is: a) Did the Himyarite Kingdom have access to the Oral Torah and thus follow the relevant procedures for conversion and understanding of the Tanakh and b) If not, then would their conversion be valid in the first place (though I am aware that there were obviously Roman converts before the Oral Torah was formally put down, but I am specifically asking in the context of the Himyarite Kingdom because its a bit distant from the rest of Judea and the Roman Empire)?