It is the only piano trio he ever wrote, albeit scored for flute rather than the more conventional violin, and is one of his most substantial chamber pieces.
The composition process can be traced from entries in Weber's diary: on 8 April 1818 he "worked on trio"; on 12 May he probably began composing the finale rondo (in Dresden).
These is an assumption that it was derived from Adagio with Variations for cello and piano, J.Anh.42 (composed in 1813 in Prague), a work today lost.
The first edition (only instrumental parts) was published by Schlesinger in Berlin in 1820 (plate number 1053): he sent the first two engraved copies to Weber on 21 July 1820.
There is an alternative version with violin instead of flute, published posthumously, and thus scored for a more conventional piano trio.