The situation at Tobruk from mid-September 1941

Once the decision had been made to relieve the 9th Australian Division at Tobruk, there was some repercussions. General Auchinleck considered that since the Australian Government seemed to have lost confidence in him, he should resign his command. That did not happen, but it was a reasonable conclusion. Part of what happened were the machinations by General Blamey to get his way, no matter the cost. The better results were the addition of an additional infantry tank battalion, 4-4.5in guns, and twelve more 25pdr guns.
General Morshead returned to Tobruk on 17 September 1941. He was informed on his arrival that while he was gone, the Germans had attacked one of the observation posts that lay outside the perimeter wire. They had used five tanks on 14 September. At the same time, they made a reconnaissance into Egypt with a force that included tanks. Rommel had called the operation "Summer Night's Dream". We have heard this translated as "Midsummer's Night Dream", which seems more like what Rommel would have called it. The Australian historian thought that since this was mid-September, midsummer was not appropriate. The historian's suggestion was that this operation gave Rommel a false sense of what the British were doing and what they were thinking.
For the coming battle between Axis and British forces, the Germans incorporated responses to lessons learned from Operation Battleaxe. They extended their defenses for some 25 miles south of the Halfaya Pass area. They had battalion-sized units to hold each fort that was built. Given the success of using 88mm anti-aircraft guns against British tanks, they included the use of those guns with armored forces for the next battle, The Germans also started using radios follow the message traffic in their own units and also started using front-line signals intelligence to intercept and process British communications.
The Germans also worked at pulling their battle-group ad hoc organization back into formal division organization. They had two complete armored divisions, the 5th Light Division and the 15th Armored Division. They also had new infantry to use. They had the 361st Africa Regiment, along with two other infantry regiments. The 361st Africa Regiment included former French Foreign Legion troops.
With the Italian Trieste Mechanized Division, they had the complete Italian Mobile Corps. This is based on the account in Vol.III of the Australian Official history.