The Apostle Paul spread the teachings of Jesus primarily between
roughly 33 AD to 66 AD.
This timeframe is based on the understanding that Jesus was crucified around 30-33 AD, and Paul's ministry began shortly after his conversion, which is generally placed a few years after Jesus' death. He was martyred, traditionally believed to be in Rome, around 66 AD.
Therefore, his missionary journeys and letter writing, which are our primary sources for his teachings, fall within that roughly 33-year period.