Ok, it seems there's a need for a little explanation of both the battle and the records.
On the evening of the 19th July, Australian and British troops made an advance against the German lines. In a few places they were able to occupy the German trenches and push beyond. These troops managed to hold the captured trenches overnight against shelling and counter attacks but by the morning of the 20th, the positions had become untenable and they had to retire back to their starting positions - handing back the captured trenches to the Germans.
The bodies of the soldiers who fell between the lines in no-man's land remained there for several years until war's end when Graves Registration Units were finally able to recover them. Unfortunately, by that time they were unable to be individually identified and were buried in surrounding cemeteries like VC Corner and listed as 'Known Unto God'.
However, the bodies of those who had fallen in or beyond the German lines were collected by the German troops and buried at Pheasant Wood (amongst other places). This was done in the days immediately after the battle mainly due to the risk of disease etc. Fortunately, the Germans removed all personal items and ID disks and recorded the details. Although the actual lists are nowhere to be found, individual German vouchers are evident in the service files of almost all these soldiers. Unfortunately for the British, almost two thirds of their WW1 records were destroyed during the blitz of WW2 and there is no clear way of establishing a defined list beyond those who went missing during the battle. Hence, their potential list is far larger than the Australian one and has no certainty.
The Australian documents have a variety of dates of death purely because in most cases they weren't sure whether the soldier had died on the 19th or 20th. In fact, to begin with, they thought that many of the men had actually been captured and it was only months after the battle that it was decided by way of Red Cross enquiries and German notification that these men had actually been killed. Thus, in many cases a nominal date was chosen and generally given as the 20th because this was when the battle ended and casualty counting began.
In fact, there are a number of these men listed as having been killed on the 21st July most likely because that's the first opportunity that particular battalion had to call the roll and record casualties. We now know that these men were killed during the battle but their names don't appear on any memorial at Fromelles and are instead on the Villers Brettoneux Memorial.
Further to that, one particular Australian has an official date of death as about September 1916, supposedly as a POW. This anecdotal information was given to the family fourth hand by someone who knew someone etc. and as a result was eventually recorded as such by the authorities. We now know this was completely wrong.
The German documents all say the 19th but this is because they record them from the date the battle began. They too would be unsure exactly when each Allied soldier was killed as they only recovered the bodies at the end of the battle when they were able to reoccupy their lines. I think it fair to assume that when they state "fallen at Fromelles on the 19th July", they are actually making reference to the battle which began on the 19th.
I hope this has cleared up a few questions. I wouldn't be too concerned with which side says what date as both were just estimations. Probably the best option would be to say they died on the 19/20th July.
I hope this has helped.
Cheers,
Tim L.