Ilaria Ramelli at the Catholic University of Milan in the HUGOYE: JOURNAL OF SYRIAC STUDIES:
Abstract: “The Teaching of Addai is a Syriac document convincingly dated by some scholars in the fourth or fifth century AD. I agree with this dating, but I think that there may be some points containing possible historical traces that go back even to the first century AD, such as the letters exchanged by king Abgar and Tiberius. Some elements in them point to the real historical context of Abgar ‘the Black”s reign in the first century. The author of the Doctrina might have known the tradition of some historical letters written by Abgar and Tiberius.”
For instance:
Whereas the legend of Abgar’s letter to Jesus and of the latter’s response is absolutely unhistorical—even the date given is incorrect,51 and Eleutheropolis did not have this name in the first cent.52—, the correspondence between the Edessan king and the Roman emperor might contain some historical traces.