The Jabirian corpus is not mentioned in any source before around 900 CE; the first biographical account is the Baghdadi bibliographer Ibn al-Nadim's Fihrist (987), written more than a century after Jabir's purported death, and some 10th century scholars already denied that Jabir had ever existed. Modern scholarship generally treats the name Jabir ibn Hayyan as a pseudonym used by one or more anonymous Shi'ite alchemists writing in the late 9th and early 10th centuries, so no reliable birth or death date for a single historical author can be established; reported death dates range from 806 to 816 CE and rest on late, mutually inconsistent reports.
What would resolve this A securely dated, independently corroborated primary source placing a historical Jabir ibn Hayyan's birth, death or documented activity would resolve the question. Short of that, a settled scholarly consensus on the dating of the earliest core layer of the Jabirian corpus, as distinct from its 9th to 10th century redaction, would narrow the range.
OpenHistory of science; Islamic manuscript studiesJabir ibn Hayyan (Wikipedia)