Dear Mr. Moffa,
Thank you for posting your request on History Hub!
According to the Nationality Act of 1940 Section 320, a person not an alien enemy, who resided uninterruptedly within the United States during the period of five years next preceding July 1, 1920, and was on that date otherwise qualified to become a citizen of the United States, except that such person had not made a declaration of intention required by law and who during or prior to that time, because of misinformation regarding the citizenship status of such person erroneously exercised the rights and performed the duties of a citizen of the United States in good faith, may file the petition for naturalization prescribed by law without making the preliminary declaration of intention, and upon satisfactory proof to the court that petitioner has so acted may be admitted as a citizen of the United States upon complying with the other requirements of the naturalization laws.
In general, naturalization was a two-step process* that took a minimum of five years. After residing in the United States for two years, an alien could file a "declaration of intention" ("first papers") to become a citizen. After three additional years, the alien could "petition for naturalization" (”second papers”). After the petition was granted, a certificate of citizenship was issued to the alien. Your relative may not have completed the process.
You may wish to review these websites History of the Certificate of Naturalization (1906-1956) for additional information and/or resources.
We hope this is helpful. Best of luck with your family research!