Dear Ms. Burgess,
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The Federal Government does not ordinarily create or maintain birth, death, marriage or divorce records. Such records are made and kept by State and local governments rather than the National Archives. We suggest that you search the Illinois Deaths and Burials, 1749-1999 FamilySearch index and review the FamilySearch Research wiki for Illinois Deaths and Burials.
We suggest that you contact the Illinois Department of Public Health to request a search for the death certificate. You may wish to note any name variants or broaden your search for the surrounding years.
We also suggest that you review the FamilySearch Research wiki for Illinois Genealogy, as well as NARA’s Resources for Genealogists. Also, the History Hub Blog titled Suggestions and Advice for Family History Researchers and the FamilySearch Research wiki for United States Genealogy may be useful.
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Unfortunately the supplied details are rather sparse. By throwing the net a bit wider and creating a rough layout I think that I’ve located one death for you. Hopefully this layout might help someone else.:
John TIMOLAT b abt 1885 New Jersey
X Laura CRAGG (nee SHIRE) b abt 1883 Illinois
==> In 1940, the couple is still in Chicago, Cook IL (https://www.familysearch.org/ark:/61903/1:1:K4M5-HZ9), but they can be found in the 1955 Joliet (Will, IL) directory, so their death must to have occurred after 1954.…
At least 3 daughters for Laura SHIRE and Edward C CRAGG:
Helen CRAGG b abt 1899 IL
X (Claude?) HEATER
Olive CRAGG b abt 1901 IL
X Phillip J BURGESS b abt 1900 IL
Beryl CRAGG b (6 Jan?) 1902 IL
X George K GARINES b abt 1900, d 19 May 1925 (https://familysearch.org/ark:/61903/1:1:QL4R-QKTT)
==> I suspect that Beryl remarried somewhere in the mid 1940’s to an Arthur Prentice McCRADY b 1907, d 1946 (https://www.familysearch.org/ark:/61903/1:1:NQH1-SL1).Beryl McCRADY turns up in in the 1947 Joliet directory. In the 1950’s she’s mentioned as the manicurist in “Richard’s Cut & Curl Beaty Shop”. NB Olive BURGESS was listed as the beauty opr for this same place in 1940’s.
Beryl McCRADY dies in May 1980. Last Place of Residence: Will, Illinois (https://www.familysearch.org/ark:/61903/1:1:J1CR-TZD)