The family group sheet matches my info almost exactly.
I checked the 1875 Minnesota census (now online at ancestry.com) and find John Moberg, 49, b. Sweden; Catharina, 41, b. Sweden; August, 12, b. Sweden; Carolina, 2, b. Minnesota all on the Fish Lake Twp., Chisago Co. census. Ages match very nicely. By 1880 they are in the Douglas county census. My brother lives quite near Harris btw. May be worth a trip up there and check out cemeteries or churches.
The Frykstrom name first appears when Erik Nilsson is at Uddheden, Soldate Bastalet in 1814-9 exam and is listed as Erik Nilsson Fryk. In 1819-23 exam it is spelled Fryx. Thereafter Frykström. One relative of ours thought the name was given to him as a rank of honor, being a ship's captain. Imaginative, but completely lacking in any substance. You mentioned Jag on exam being a hunter. I believe the actual occupation would be Faltjagere. Field hunter (?) or soldier.
All for now