There is a mis-print/error in the Russian order of battle provided by the author.
In the Russian 3rd Corps of the Army of the Danube, the author has "10th Jaeger Regiment, Lieutenant Colonel Verbovski I". This should be ….
10th Artilllery brigade – commander lieutenant colonel Platon Vasil'yevich Verbovskiy-1
--- 10th Battery company – commander lieutenant colonel Lev Maksimovich Shul'man-3
--- 18th Light company – commander lieutenant colonel Fyodor Borisovich Gine
--- 19th Light company – (commander lieutenant colonel Verbovskiy) in command staff-captain Stepan-Stepanovich Romanov-3
The Army of the Danube came into the area of operations of the Polish Bug division toward the end of September 1812, and marched on to take Brest-Litovsk on the 29th. If the Polish side recalled a "Battle of Pawlowice" that occurred with general Voinov's 3rd Corps on 23 September, it was not a battle that the Russians noticed or recorded. I imagine that the Polish Bug division wisely decamped when an entire Russian Army, veterans of the recent Turkish war, was about to march over them. For the Russian Army commander's report, see : link
The placenames mentioned by the author may be easier to find with their current names ….
Places now in the Ukraine
--- "Uscilug" / Ustyluh / Устилуг
--- "Vladimir" / Volodymyr-Volynskyi / Володимир-Волинський
--- "Sadowa" / Vil'ka-Sadivs'ka / Вілька-Садівська
--- "Pawlowice" / Pavlovychi / Павловичі
--- "Swiniuchy" / Pryvitne / Привітне
--- "Beresteczko" / Berestechko / Берестечко
--- "Lutsk" / Lutsk / Луцьк
--- "Luboml" / Liuboml / Любомль
Places now in Poland
--- "Zamosc" / Zamość
--- "Hrubieszow" / Hrubieszów
--- "Dubienka" / Dubienka
--- "Wlodawa" / Włodawa
During the months before the Army of the Danube's arrival, there were quite a few small actions involving the Polish Bug division : raids, counter-raids, river crossings, reconnaissances, etc. stretching over more than 100 km of the Western Bug. The Russians threatened to raid deep enough to burn Chelm or Zamość, and the Polish threatened to get into the rear area lines of communication of the 3rd Reserve Observation Army.
The opposition to the Polish Bug division was general Krushchov's border detachment:
detachment commander shef of the Arzamass Dragoon regiment major general Ivan Alekseyevich Krushchov
--- brigade adjudant lieutenant of the Arzamass Dragoon regiment Yuriy Petrovich Ratiyev
--- provisional adjudant officer candidate of the Arzamass Dragoon regiment Ivan Osipovich Bartenev
Zhitomir Dragoon regiment : 4 squadrons, ~480 men, initially located in/near Kovel' with one squadron forward at Liuboml
--- shef colonel Ivan Andreyevich Argamakov-2
--- squadrons : major Kulyabka, lieutenant colonel Gavrila Ivanovich Stepanov-3, lieutenant colonel Andrey Nikolayevich Kaverin, regiment commander lieutenant colonel Konstantin Stanislavovich Snarskiy
Arzamass Dragoon regiment : 4 squadrons, ~560 men, initially located in/near Volodymyr-Volynskyi
--- in command major Ivan Andreyevich Bartenev-3
--- squadrons : major Koltovskiy, major of the Tver Dragoon regiment Arshukov, major Turchaninov, major Dlatovskiy
Don Cossack Chikilyov-1 regiment : 5 sotni, ~450 men, initially patrolling the south part of the Polish border region from Liuboml to the Austrian border
--- commander major of the Cossack host Aleksandr Fyodorovich Chikilyov-1
1st Astrakhan Kalmyk Cossack regiment : 5 sotni, ~480 men, initially patrolling the north part of the border region from Liuboml to near Brest-Litovsk
--- advisor major of the Kazan Infantry regiment Ivan Vasil'evich Dublyanskiy-2
--- commander captain noyon (Kalmyk prince) Dzhamba-taysha Tundutov
one recruit company from the 4th reserve battalion of the 10th Jäger regiment : 2 platoons, ~150 men, apparently "detained" by the general Krushchov as they marched from the Izium recruit depot (Kharkiv region) to join the active battalions of the regiment serving near Brest-Litovsk as part of general Lambert's avant-garde of the 3rd Reserve Observation Army
--- platoon commander ensign of the 10th Jäger regiment Linevich
--- platoon commander ensign of the Malorossia Grenadier regiment Tolbuzin
district invalid commands : each 25 to 50 men, retired soldiers serving as local internal security
--- in Lutsk, Volodymyr-Volynskyi and Kovel'
Total for the Russians of about 2200 men, mostly excellent cavalry, and no guns(!) …. vs. about 5600 "second-line" troops and 8 guns for the Polish Bug division.