Nichiren taught the Specific Transmission as the transmission from the Original Buddha Shakyamuni to Bodhisattva Jogyo. Nichiren taught the General Transmission as the transmission from the Original Buddha Shakyamuni to the Bodhisattvas of the Earth.
The Specific Transmission does not refer to a transmission from Nichiren Daishonin to the Nichiren Shoshu priests, to Daisaku Ikeda, nor the Three Presidents. The General Transmission does not refer to the Nichiren Shoshu priests nor the three presidents transmitting the Law to their disciples and believers.
They fabricated their teachings on the transmission in order for the self serving agenda of money and power. They make the transmission appear other than what the Lotus Sutra and Nichiren taught.
Nichiren Daishonin' explanation of the transmission accords with the Lotus Sutra's. Nichiren Shoshu's and SGI's does not.