I’m looking at Michael the Syrian, and in the first volume of the French translation, I find the following:
Note by Theodosius of Edessa. — You should know that Eusebius, in the Chronography he wrote, began with Abraham the Canon of years and continued until the year 20 of Constantine. But James, of the city of Edessa, who transcribed the book from Greek into Syriac, added the dates and coordinated the events not only from Adam to Abraham, but also from Constantine until his time, when there reigned over the Romans, Justinian, and over the Arabs, `Abdallah. He carefully reviewed all the Chronicle, both about the empires which Eusebius ignored, and because of other things that this venerable [Jacques] commemorates. And when he starts to dispose them by year, he ties the year 20 of Constantine to the year 21. — As for us, so that the computation is not disturbed after the Canons of Eusebius we put those that Jacques himself has made.
Like so much of what Michael quotes, the history of Theodosius is not extant.
Comparing the introduction to James, printed by Brooks in the CSCO text, with Michael’s quotes, it is clear that Brooks has more of James’ words than Michael the Syrian does. There are a dozen pages of introduction, all interesting, but probably beyond me to translate at this time.