Okay, that helps. So diamond cutters are kind of a red herring, in a sense. What you are seeking is Jennie's birth certificate. The first route I'd go if I were you is: follow the family. Who are Lena Feldman's parents? siblings? Where/how did she meet her husband? and where did she marry him? Jennie's birth was shrouded in secrecy - but was that also true regarding Lena's life, and information about Lena's extended family? Usually a woman immigrating (in this case from Russia/Poland) would be traveling to a family member in the USA, so presumably Lena was not alone in New York. Also, do you know that Lena was her name? I've seen Lena as a nickname for Carolina, or her name could be Liya, etc. Has your friend checked the family history photos for names? Saved letters? I am curious how the unknown biological father of Jennie could be known to be a diamond cutter or importer, given the story about the secrecy and all papers being destroyed after Jennie died. That seems very odd, that the one fact - his occupation - would be known. HOWEVER that's a side issue, and does not lead you to the birth certificate. It's very kind of you to try to help your friend.
Here's a link to a list of Feldmans in St. Louis 1891-1910:http://genforum.genealogy.com/feldman/messages/181.html
Jenny could be living with a relative of Lena's near Lena rather than living in New York. Finding her in 1900 would be great, but most likely won't solve the birth father problem. Oh - Jenny could also be a nickname - for Genevieve, Jennifer, Geneva, Zlate, etc.
Feldman can be found as Feltman, right? Other variations? FYI, in case its news, you can use * as a wildcard when searching on Ancestry.com. Fel*man brings up both Feldman and Feltman.