Sulaym ibn Qays was actually dead by 714. So he wrote his hadith book before … dying?!, that is, before Muwatta.
Historiography of early Islam - Wikipedia, the free encyclopedia
The Book of Sulaym ibn Qays; by Sulaym ibn Qays(death: 75-95 AH (694-714)). This is a collection of Hadith and historical reports from 1st Century of the Islamic calendar. Sulaym ibn Qays is the first Shia author in “al-Fihrist” of Ibn al-Nadim.