Johann Mederitsch – Wikipedia composed the 1st Act.
Johann Georg Anton Mederitsch, called Gallus-Mederitsch (baptised 27. Dezember 1752 in Wien; † 18. Dezember 1835 in Lemberg), was an Austrian composer, conductor and teacher.
Peter von Winter composed the 2nd Act
The intention to follow-up to the succes of Magic Flute with an effectful title was surely a pure motive of Schikaneder.
There have been attempts to follow the success of Magic Flute without direct relation to the story: Die Waldmänner (1793, Henneberg), Der Höllenberg (1795, Wölfl), Der Spiegel von Arkadien (1794, Süßmayr).
A real sequel was tried by Goethe but composed and performed 100 years later in 1891 with “Sarastro” after enlarging Goethe´s fragment to a libretto by Gottfried Stommel.
For the celebration of 100. year after Mozart´s death the Liszt student Karl Eduard Goepfart performed this sequel in Hengelo/NL.
So Schikaneder recognized this potential of good sequels and engaged Johann Mederitsch to compose Act 1 and Peter von Winter for Act 2, finally the performed it already in 1797: Die Pyramiden von Babylon.
First performance 25. Oktober 1797 Freihaustheater auf der Wieden Wien.
Aufführungen im Ständetheater von Prag 1815-06-23 und 1815-06-27
https://lccn.loc.gov/2010661002
libretto Hamburg : Gedruckt bey Johann Gottfried Müller, 1807.