What I have found :
Kaisersteinbruch was a training area.
Panzer-Kompanie (Fkl) 316
The Panzer-Kompanie (Fkl) 316 was formed on 1 April 1943 and equipped with 10 StuG III as control vehicles. In September it was attached to Panzer-Lehr-Regiment 130 of the Panzer-Lehr Division and was reequipped with Tiger I control tanks. In January 1944 it was ordered to be reequipped with Tiger II tanks and was redesignated schwere Panzer-Kompanie (Fkl) 1. In June 1944 became the first company of Panzer-Abteilung (Fkl) 302 and left its Tiger II tanks in the Chateaudun area and was reequipped with StuG III.
Tank #12 from the company was donated by France to Sweden in 1947 where it was used for testing, ending its life being used for target practice in 1949. Its hull was scrapped but the turret remained in storage until the late 1980s when it was finally scrapped.
The "(Fkl)" in the name was for "Funklenk", a reference to the radio-controlled demolition vehicles used.
April 1943 - Formed in Eisenach
End of September 1943 - Transfer to Fallingbostel training ground and attachment to Panzerlehrregiment 130
1 February 1944 - 3 Tiger I's have been delivered when the Panzerlehrdivision requests to equip its Funklenk company with Tigers rather than StuGs
19 February 1944 - Ordered to form with Tiger IIs
14 March 1944 - Equipped with 5 Tiger IIs, but retains Tiger I's
1 June 1944 - 3 Tiger I's and 3 Tiger IIs operational
11 June 1944 - Tiger IIs handed over to crews from the Panzerlehrdivision, all Tigers lost
2 July 1944 - Transfer to Reims, redesignated as 1./Pz.Abt.(Fkl) 302 and rebuilt with StuGs
Cheers,
Rich