As near as I can tell, Arthur Casben is the forefather of all the Australia Casbens.
Arthur was born in Lambeth, London, May 1886,  He was one of eight children born to Reuben and Elizabeth (Neyland) Casbon. Arthur was a “Meldreth Casbon,” descended from John Casbel of Meldreth. His 2nd great-grandfather Thomas Casbon was my 5th great grandfather.
Arthur’s father Reuben adopted the C-A-S-B-E-N spelling of the name. This spelling appears on birth registries for his children as well as various other documents.
I don’t know exactly when Arthur left England for Australia, but I’ve been able to put together the following bits of information.
Arthur’s wife Leonora and two sons Wilfred and Noel departed from London aboard the ship Themistocles in April 1914.  The ship was bound for Brisbane, Australia, and the manifest indicates that they intended to become permanent citizens of Australia.
Leonora’s sister Helena (Ackerman) Skinner (b. 1870) was on the same ship with her six children.  Her husband, Alfred James Skinner, was not on the manifest, but at some point he also went to Australia.
They were preceded to Australia by Leonora’s parents, who departed London bound for Brisbane in November 1913. They also intended to make Australia their home. 
Leonora’s brother, Leopold Patrick Albert Ackerman (b. 1879) probably was the first to arrive in Australia. He married Mary McAdam in New South Wales in 1912.  I don’t know when he arrived in Australia.
The first Australian record I have for Arthur is his embarkation in December 1915 to serve with the Australian Forces in World War I. He was already a resident of Coogee, New South Wales. 
It’s apparent that the Arthur and Leonora’s decision to move to Australia involved Leonora’s extended family. I don’t have enough information to know what led to the decision.
My father corresponded with Arthur’s son Noel (1912-2001) in the 1990s. Noel sent a brief summary of the family’s early years in Australia, part of which is transcribed here:
My father was the only one of four brothers … who migrated to this country. He & of course my Mom arrived during 1914 when I was about 2 y.o. and with brother Wilfred 2 yrs my senior and no longer with us. My first memory of life is just before Feb. 1915 when my sister was born when we live at SCOGEE a beachside suburb of Sydney. I do not remember my Dad going to war in Palestine nor coming home in 1917. Nor do I remember going with the family to a country town in N.S. Wales where my Dad did a mail run. I do remember very vividly a bonfire being lit in the main street of Coolamon on armistise day 1918 Dad was no business man so the mail run went and we returned to Sydney. 
Besides Wilfred and Noel, Arthur and Leonora Casben had at least five more children after arriving in Australia. Some of their descendants have reached positions of prominence.
This blog occasionally gets visits from someone in Australia and New Zealand. If any Casben descendants are reading this, please feel free to contact me or leave a comment.