François-Claude Théremin was born in Prussia, the eldest son of a pastor. He trained in Magdeburg, Paris and Hanau as a goldsmith and enameller before working in Berlin with his future father-in-law, Jean-Guillaume Krüger, known for his designs for Frederick The Great's table snuff boxes. His success as well as that of his brother is largely due to his younger brother Pierre-Etienne Théremin who eventually set up in St Petersburg in 1793 and married Marianne Duval, daughter of the leading foreign jeweler and retailer in St Petersburg. This connection gave them access to the an elite clientle and notably the Imperial court whom they supplied with gold boxes, jewelry and objects of vertu. Stylistically the Théremin's boxes are closer to Geneva boxes than to those produced in Hanau or St Petersburg (Julia Clarke, 'Swiss Snuff Boxes 1785-1835,' in: Haydn Williams, Enamels of the World, The Khalili Collections, London, 2009, p. 305).
For another near identical box see The Property of a European Collector, Christie's, Geneva, 14 November 1995, lot 103. Sadly the marks are only described as 'prestige marks' but the design and colours are identical to our box.