The following comes from Alfred Rubbel
Transportation to the southern sector of the Eastern Front began on 21 December 1942. Detraining from the railroad transports which had been routed for express movement took place at Proletarskaja. The war began for schwere Panzer-Abteilung 503 in the early days of January 1943 along the Manytsch River.
Schwere Panzer-Abteilung 502 had also been organized at nearly the same time as schwere Panzer-Abteilung 503. It also had only two tank companies. In the fall of 1942 it had been commited to action in the northern sector of the Eastern Front with a Headquarters Company, a Maintenance Company and only one tank Company. The 2./schwere Panzer-Abteilung 502 had been held back at Fallingbostel. In December of 1942 the 2./schwere Panzer-Abteilung 502 loaded onto rail transport to Heeresgruppe Don. On arrival it was attached to 17. Panzerdivision and saw it's first employment in the Kalmuck Steppes southeast of Rostov under it's company commander Hauptmann Lange.
The 2./schwere Panzer-Abteilung 502 possessed a fairly good capability to operate on its own. In order to be logistically self sufficient it had been provided with the requisite additional elements. The 2./schwere Panzer-Abteilung would have liked to keep that status. For reasons of practicality and necessity the 2./schwere Panzer-Abteilung was consoldiated with schwere Panzer-Abteilung 503 as the 3.Kompanie at the beginning of January 1943. Schwere Panzer-Abteilung 503, of course, was also employed on the Kalmuck Steppes at the time. The OKH decision was not greeted with a lot of enthusiasm by the company.
With that addition, schwere Panzer-Abteilung 503 became the first Tiger battalion to be brought to full strength according to the 1943 standard of organization.
Tigers in Combat I (Wolfgang Schneider) puts the 2./s.H.Pz.Abt.502 at the following locations at the dates indicated:
05./06.01.43 - Detrainment in PROLETARSKAJA
07.01.43 - Attachment to 17th Panzerdivision. Relocation to SSUNGAR in the KUBERLE region (107 km road march without breakdown, with a maintenance stop every 20 km.)
08.01.43 - Counterattack with one company of Panzerregiment 39 on OSSERSKIJ and NISH-SSEREB JAKOWKA. 2 tanks and 8 anti-tank guns destroyed.
09.01.43 - Enemy positions with 5 Pak destroyed near ILOWASKIJ then attack on BRATSKIJ, 2 Pak knocked out. March back to PROLETARSKAJA
10.01.43 - Defense near BUDJENNY, 1 KV-1, 3 T-34s, 7 T-60s and 2 Pak knocked out. The operational tanks (3 Tigers and 6 Pz.IIIs) are attached to 16th Infantriedivision (mot).
14.01.43 - The Tigers cover the disengagement of 16th ID (mot) (3km from NOWO SSADKOWSKIJ to KAMAROW) and rejoin the company at PROLETARSKAJA the following day.
16./17.01.43 - The Pz.IIIs in covering positions at STALINSKI-PUD. Order to move to ROSTOV.
22.01.43 - Arrival at ROSTOV and integration into schwere Panzer-Abteilung 503 as the 3rd company.
The Tigers arriving from from 2./s.H.Pz.Abt.502 were most likely still painted RAL7021 "Schwarzgrau" although field improvisations are possible. 502 numbering consisted of white outlines.
Refer back to picture 1 of the series I posted above. Note the Pz.III stowage bin.
"Tigers in Combat I" (Wolfgang Schneider) dates the series of 332 pictures Oct 4, 1943. I don't have a second source to corroborate this date though.