In the household register for Undersåker in 1889 these dates are given för the family:
Gustaf b 12 Aug 1857, Stavnäs
Anna, wife 27 April 1869, Kall
Johan Adolf b 5 Feb 1888, Kall
Anna b 9 Aug 1889, Undersåker
Looking in the birth book for Stavnäs, I cannot find any Gustaf born 12 August, but there is one born 12 September 1857, son of inhyses (person renting a house or part of it) Johan Persson and wife Anna Jonasdotter at Svanickeboda. In the household census (Stavnäs AI:19, p 289) the family is listed:
Johan Persson 28 Dec 1822, (all are born in Stavnäs)
Anna Jonasdotter 23 Sept 1822
Christina 14 Dec 1850
Carl August 27 June 1853
Johan 6 Sept 1855, dead 17 Feb 1856
Gustaf 12 Sept 1857
I belive this is the right family, they move to Brunflo in Jämtland 1858. The place Linehäll is mentioned here, but there is no immigration book for Brunflo in 1858. However, I find them in the census of 1860 (only available for Jämtland):
Johan Persson is a stattorpare (gets a small cottage and some land in exchange for work at a larger farm), they have one more son born 6 May 1860. Here Gustaf´s date of birth has been changed to 12 August 1857! A misprint in the books!
In the 1880 census Johan Persson and family, now with only younger children live at Haga in Lockne parish in Jämtland. They have daughter Hilma Maria b 1862 in Lockne and son Axel Otto born 1866 in Brunflo. (Dates and places should be checked).
The household census shows that the son born in 1860 (Erik Wilhelm?) has become a soldier.
Gustaf is now working as a farm hand in Lockne, at Haxäng farm. He came there in 1880 and leaves in 1883 to move to Offerdal. His date of birth is given as 12 Aug 1857 here too.