I haven't got information om the foot battery at hand, but in early 1815, the two (!) horse batteries were taken over in Prussian service as Reitende Batterie No. 18 and Reitende Batterie No. 19.
In early 1815, batteries 18 & 19 were reorganised to Prussian standards. The Russian 6pounder guns and 10pounder unicorns were kept. The ammunition boxes on the limbers were enlarged. The ammunition wagons were replaced by French ones. The old and used Russian harness was completely replaced by British harness. New uniforms were distributed following Prussian patterns (probably yellow shoulder-straps, as they both now belonged to the 3rd – Silesian – artillery brigade), but the black leather belts were kept (as well as the Russian shakos I believe). All this was completed by the end of April 1815.
These two batteries had a "Park-Kolonne" of their own, with Russian ammunition: "Park-Kolonne No. 19" of 12 ammunition waggons.
I was unable to verify the plate by Herbert Knötel in Elting's Napoleonic Uniforms, which pretends to show the "Reitende Batterie No. 18" (Prussian plate 47, p. 536).
What is definitely wrong for the horse battery no. 18 are the white leather belts. Instead, the black belts of Russian origin were kept. Strotha's work on horse artillery as well as his regimental history of the 3rd artillery brigade are definite on this. I would have expected the shoulder straps to be yellow as well.
Therefore I am sure that the caption for this plate is wrong.
There was another horse battery which actually had Tarleton helmets: In April 1815, the half horse battery No. 13 of four guns, was augmented to a full horse battery, and according to Strotha its men received British uniforms of the horse artillery. So Knötel's image can't be horse battery no. 13 either, but mightbe he mixed up some of his notes.
On a parade in August 1815, even the officers of this battery appeared with British helmets, to the disgust of the Prussian king who ordered to take them off immediately (for the officers only).