Have you looked for her as Rifke/Rivke? I doubt she entered the US as Rebecca.

Barbara Mannlein
Tucson, AZ

Is this the correct person? Manifest says she is going to Lazar Grunberg

Name:	Rebeca Braunstein
Arrival Date:	5 Dec 1905
Birth Date:	abt 1888
Age:	17
Gender:	Female
Ethnicity/ Nationality:	Roumanian (Romanian)
Port of Departure:	Le Havre
Port of Arrival:	New York, New York, USA
Ship Name:	La Gascogne

At 18:07 05/07/2020, dasw5 via groups.jewishgen.org wrote:

Is this the correct person? Manifest says she is going to Lazar Grunberg
Name: Rebeca Braunstein
Arrival Date: 5 Dec 1905
Birth Date: abt 1888
Age: 17
Gender: Female
Ethnicity/ Nationality: Roumanian (Romanian)
Port of Departure: Le Havre
Port of Arrival: New York, New York, USA
Ship Name: La Gascogne

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I do NOT know that there is a connection here, but.....
I am working on Florence Marmor's cemetery records and have listed there

Mokkom Sholom
Braunstein Rebecca  
born      21 May1888  
Monument
Rivka Braunstein daughter of Avram Meier (?) Reuben (?), died 05/18/1888.  (#18 mish mash row)  death cert #15807, died 05/18/1888 at 11 Rivington St., New York, N.Y. of septicemia and peritonitis after childbirth, age 27 years, 7 months and 6 days, born Roumania, U. S. and New York 13 days, father Abraham Gershon, +mother Nache Gershon, both parents born Roumania, buried 05/21/1888, undertaker Jacob Finkelstone, 343 E. 52nd St., New York, N.Y. 
Note: Birth Certificate index   Rubin Braunstein born 13 May 1888, cert #13655M, to Rachel and Jacob Braunstein of 11 Rivington St., New York, N.Y.  Birth certificate #13655M, born 13 May 1888 at 11 Rivington St., New York, N.Y., mother's maiden name Rachel Gersen, born Roumania, age 27 years, father Jacob Braunstein, birthplace unknown, age 34 years, occupation agent, 1 child born prior and alive at birth, L. or S. Winerowitz, 284 Suffolk St., New York, N.Y.  Death certificate #19647, Reven Braunstein, died 06/24/1888 at Infants Hospital, Randall's Island, New York, N.Y. of inanition and marasmus, age 1 month and 14 days, born New York City, both parents unknown, both parents birthplace(s) unknown, no burial information listed on cert

Search & Unite attempt to help locate people who, despite the passage of so many years since World War II, may still exist "out there".
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Shalom!
 Not sure if this Rebecca is the right one? Her age more or less matchs, but she came from Stanislaw Austria. My grandmother had cousins in New Jersey who were in the butcher business..(in Newark, New Jersey) 1950-1960s. One of them was MAX BRAUNSTEIN! Have no idea who Lazer Grunberg was!?