These Prussian 2/3 battalions mentioned were created by general lieutenant v. Rüchel (in his corps only) on 1 October 1806
He ordered that the regiments in his corps should be reformed in three battalions of two ranks only. The 1st and 3rd battalions of 3 companies in 6 platoons, with one cannon each, the 2nd battalion of 4 companies in 8 platoons with two cannons. However, he envisaged to combine the regimental guns of a brigade to form a brigade battery.
Some more info on the Prussian regimental organisation in 1806: here: