Good find, David, especially since the surname was mistranscribed as Hyam on the SynagogueScribes site.
However, Charlotte Styer's maiden name Levy, not Phillips. What makes you think that she was the daughter of Levi and Haya?
Are you thinking that she used her father's given name as a patronymic surname?
Added: The maiden name of the Styer children's mother was recorded as PHILIP, not LEVY.
I think that nails it. Great detective work, David