Did Ja'far al-Sadiq teach all four Imams, and is he the source of the four schools of thought?

Jafar ibn Muhammad ibn Ali ibn Al-Husayn was an Imam from the Imams of Ahlus-Sunnah. Abu Hanifa and Malik took knowledge from him, but he was not the sole source of their knowledge. As for Al-Shafi'i and Ahmad, they were not born until after his death, as Jafar Al-Sadiq passed away in the 148th year of the Hijra, while Al-Shafi'i was born in the 150th year of the Hijra, and Ahmad in the 164th year of the Hijra.