Rachels burial info at Find a Grave shows her parents as Wolf and Henrietta Levi so I took that info and found marriage for Henry and Rachel
Henry Cohen New York, Marriages, 1686-1980 marriage: 03 Jun 1877 Manhattan,? New York,? New York parents: Isaac Cohen,? Jeanette Abrahms spouse: Rachel Levi groom's name: Henry Cohen bride's name: Rachel Levi marriage date: 03 Jun 1877 marriage place: Manhattan, New York, New York groom's father's name: Isaac Cohen groom's mother's name: Jeanette Abrahms bride's father's name: Wolf Levi bride's mother's name: Henriette Cohen indexing project (batch) number: M00170-2 system origin: New_York-ODM source film number: 1562182
************* I then went to England census to find Henry with parents Isaac and Jeanette but have not been able to find them
I am now wondering if perhaps Cohen was not Henry's birth name ? Maybe his parents changed their name when they came to US ?
Of course I don't know if his parents came to US - could Henry have changed his name??