Many UK families have stories of an ancestor hung or transported for stealing sheep; how many are true however is difficult to know.
Felons were transported to what is now USA prior to the Revolutionary War and thereafter to Australia. See
http://en.wikipedia.org/wiki/Penal_transportation and also
http://en.wikipedia.org/wiki/Convicts_in_Australia South Africa was not a British penal colon y (though there were attempts to use West Africa as one: see
http://www.historytoday.com/blog/2012/01/merciless-place-bri... ).
The diamond mining era in South Africa post-dated penal transportation - the rush began in 1869 (see
http://en.wikipedia.org/wiki/Kimberley,_Northern_Cape#Discov... ) whereas British penal transportation to Australia ended in 1868.
Many UK families have stories of ancestors who emigrated and got rich and many UK families have stories of tragic losses of the resulting wealth.
There may well be truths underlying the stories but there is a frequent tendency to exaggeration.