I assume you already checked variant spellings of FLEISCHMANN.
Also, you should take into consideration that given names were often
"Americanized" once the immigrant settled-in. Channe could easily become
Hannah or Anna.
Do you know where they lived in the US? If in NY, there was a 1905 census as
Name change due to marriage is also a possibility. If they lived in NYC,
marriage records are available online.
snip...I would appreciate your kind help in my FLEISCHMANN family originally from
Tarnopol, who immigrated to the US at the beginning of the 20th century.