Re: How do I use the "Declaration of Intention" to find the actual naturalization papers? #records
If you do a keyword search of the FamilySearch catalog (ex: "new york southern declaration"), you will see that they only have two collections of Declarations from the US SDNY court: 1845-1911 and 1924-1925, so your grandfather's declaration in 1922 is not available at FamilySearch.
You can pay to receive a copy from NARA NY once they resume services, post-Covid: https://eservices.archives.gov/orderonline/start.swe
PS: I used the information that you provided and did a search to see if I could locate his final naturalization papers (petition) and could not find anything, so it is likely that he did not complete the naturalization process.
HYMAN/HEYMAN/HEIMOWITS/CHAJMOVITS: Zemplen-Dobra, Hungary > New York; KLEIN: Satoraljaujhely (Ujhely), Hungary > New York > Los Angeles
KRONOWITH: Hungary > New York; OSEAS/OSIAS/OSIASI/OZIAS: Iasi, Romania > Chicago > Milwaukee > Los Angeles
SCHECHTER/SHEKTER: Kishinev, Bessarabia > New York; SHERMAN: Iasi, Romania > New York > Los Angeles
STRUL: Iasi, Romania > Haifa, Israel; WICHMAN: Syczkowo (Bobruisk), Belarus > Milwaukee > Los Angeles