John Stanley Caughey, 65, a prisoner at HMP Glenochiln, near Alloa, was convicted for the murder of Margaret Hunter, of Chisholm Place, Grangemouth, on August 5, 1975.
A spokesperson for the Scottish Prison Service said: "Police Scotland have been advised and the matter reported to the Procurator Fiscal. A Fatal Accident Inquiry will be held in due course."
Caughey, from Grangemouth, had sex with Mrs Hunter, a mother-of-four, and claimed that afterwards she taunted him and he lost control.
Her naked body was found brutally battered about the face and head. She had been attacked with a piece of wood and strangled.
On the same day, Caughey had abducted a woman taxi driver, Rowena Robertson, and driven her taxi away.
He tied her up with her own tights and stuffed a panty girdle into her mouth. She eventually managed to escape and he drove away only to give himself up later.