Foelsche migrated to South Australia in 1856 and was appointed Trooper 3rd Class in the Mounted Police. He married Charlotte Gorgina Smith in Strathalbyn on 5 January 1860, being appointed Sub Inspector in charge of the Northern Territory Mounted Police in 1870.
He made a systematic study of Aboriginal customs and language, which was read to the Royal Society of South Australia as "Notes on the Aborigines of North Australia." on 2 August 1881. Foelsche was a leading photographer of the Northern Territory where his work became the main pictorial record of NT Aboriginal people, scenery and industries.