K Cavanagh S IN California

I am tracing my gr-grandfather's brother (name unknown) who left BIRKENHEAD, CHESHIRE, ENGLAND in the late 1880's. My gr-grandfather was JAMES KAVANAGH and he is rumoured to have 'drowned at sea' en route to the U.S. but in recent years a couple of ladies from California arrived in Birkenhead after tracing their family. I live in Canada now and got this information 3rd hand from a recently discovered 2nd cousin. So we have assumed that the brother arrived in California. If anyone can help that would be appreciated. Thanks, Angela