This question comes up again and again. Did they work together, and then it went south for awhile?
e.g. How did Simonides end up working on Russian historical documents in St. Petersburg in the late 1860s?
Dean knew about Simonides working in St. Petersburg, here he offers another tidbit, although a bit unverified.
.Lectures on the Evidences of Revealed Religion (1890)
George Washington Dean
A curious question was raised concerning the Sinaitic manuscript soon after its discovery, and the ensuing discussion settled a number of interesting points. An audacious impostor, Constantine Simonides by name, a Greek of Syme—a worthy compeer of the famous George Psalmanazar of the last century— was first brought into notice by his fabulous history of Uranius, the son of Anaximenes. Simonides was an accomplished calligraphist, and had been employed by Tischendorf, with whom he quarrelled. When Tischendorf, in 1860, issued his first fac-similes of the Sinaitic manuscript, Simonides boldly declared that he had himself written the whole of it ...