The passport application also says Henry Zucker was naturalized in the US District Court in Brooklyn (Eastern District) on July 24, 1902. I found that record at Ancestry here, in which he said he had been resident in the US since July 1890.
NOTE WELL there is language in the naturalization document suggesting this was a "minor naturalization." That language says he arrived in the US and was resident here for three years prior to his reaching age 21. For that reason I would not expect to find any separate declaration of intention.
ALSO, the back of the naturalization document holds an important clue. It appears Henri/Henry applied for a replacement naturalization certificate in early 1943. Even though he naturalized before 1906, so INS never had a C-file for Henry before, his 1942/1943 application for a replacement would have created a special kind of C-file known as an "Old Law Replacement" certificate. The prefix for those C-files is "OL."
The information on the back of the court document on Ancestry shows Henry "applied for a new certificate" and presumably the original court naturalization record was checked/verified by INS on January 16, 1943, probably by an INS examiner (Shatzman). The file number given, "2B52123" is the INS application file used temporarily and NOT the file number needed to request records.
The records (his application and supporting documents and correspondence) will be in his OL C-file. The OL C-number is not found in this notation. It would be found on the original replacement certificate issued in 1943 (assuming it was issued), and in the INS, now USCIS, index. Sadly the only way to get to that file, if you want it, is to request it from the USCIS Genealogy Program.
This is a great example of how there can be rich records created decades later than one would expect!