I do not find him in the 1870 Georgia census, but I do find a F. M. Jackson in Arkansas, could this be him?
1870 United States Federal Census about F M Jackson
Name: F M Jackson
Birth Year: abt 1839
Age in 1870: 31
Birthplace: Illinois
Home in 1870: Pecan Point, Mississippi, Arkansas
Race: White
Gender: Male
Value of real estate: View image
Post Office: Pecan Point
Household Members:
Name Age
William Clark 33
F M Jackson 31 Farm Laborer
Rebeca Jackson 23
Lowrena Jackson 2
Franklin Jackson 6/12
Polly A Taylor 33
V T Jackson 22
James Freeman 21
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