Link to the main webpage for Charles A. Falkinburg and Nelson Hance Falkinburg
Arrival of Sarah Abigail from San Francisco to NSW Maitland Mercury, 31 DEC 1851, p. 2
Arrival of Sarah Abigail at San Francisco from New Castle (The Maitland Mercury, and Hunter River General Advertiser 5 April 1851 p 2.)
Reference to Sarah Abigail enroute to San Francisco. (New Zealander, Volume 6, Issue 485, 7 December 1850, Page 2)
Arrival Jane A. Falkinburg San Francisco (reported in Sacramento Daily Union, Volume 8, Number 1180, 4 January 1855)
Report of Charles Death in the Sacramento Daily Union, Volume 10, Number 1516, 4 February 1856 p. 2 col.2

Charles A. Falkinburg death notice also Records from Tombstones in Laurel Hill Cemetery, 1853-1927
"FALKENBURG--In this city, Jan. 31st, Capt. Chas. A. FALKEBURG, aged 31 years. New York and New Bedford papers please copy." Source: Daily Alta California, 19 Feb 1856.
Lone Mt. Cemetery "Laurel Hill Cemetery - (Lone Mountain) California, Geary, Parker and Presidio Avenue. Dedicated May 30, 1854 and moved in 1941. Originally part of Lone Mountain Cemetery and renamed Laurel Hill Cemetery in 1867. Approximately 35,000 bodies were moved to Cypress Lawn Memorial Park, 1370 El Camino Real, Colma, CA 94014, San Mateo County. (650) 755-0580"
Further exploration has revealed that the index of SF Genealogy contains reference to Jane A. Falkinburg and Charles Falkinburg. This is not an on-line resource, but merely an on-line index: http://sfgenealogy.com/sf/schellens/sff1.htm
I found the following interesting statement connecting the Connecticut Mining and Trading Company to Samuel Brannan.
"Late in the Fall of 1850 Mr. Cathn closed his law office in Sacramento, and returned to Mormon Island, being employed to settle the affairs of the Connecticut Mining and Trading Company, which was the successor in interest of the famous store and business of Samuel Brannan, and to attend to the mining interests which he had acquired in that vicinity in the summer of 1849, and winter of '49-50. Just then Wm. L. Goggin, the agent of the Post- office Department for this coast, visited Monnon Island for the purpose of estabUshing a Postoffice there. He requested Mr. Catlin to furnish a name for the office. Mr. Cathn had already formed the "Natoma" Mining Com- pany, adopting that name from the Indian dialect, it signifying "clear water, " and a tradition that such had been, among the Indians, the name by which that locality had formerly been known. Goggin adopted the name, and that section of Sacramento county was officially named "Natoma township."