Okay, the death record for Fred Sr.'s mother Alma definitely! ties the family in Illinois to the family in Minnesota (in 1930, Oscar and Alma in St. Louis County, Minnesota):
Death Record Alma Charlotte Larson died 25 Apr 1946 in Elgin, Kane, Illinois Age 58, born 04 Dec 1887 in Trymountain, Michigan. Father Louie Nelson born in Sweden Mother Marie Burquist born in Sweden Residence: Cook, St. Louis, Minnesota. Spouse: Oscar Larson Burial 27 Apr 1946 Lake St. Mem. in Hanover Twp., Cook, Illinois SOURCE: Digital Folder Number 4005315 "Illinois, Deaths and Stillbirths, 1916-1947," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/NQYW-L4H : accessed 26 April 2012), Oscar Larson in entry for Alma Charlotte Larson (1946).