Axel absolutely belongs to this family. I used the fee-based Genline site to see a parish record called the husförhörslängd (or household examination record or clerical survey record or HFL for short). That is a Swedish parish record similar in format to a census but far more detailed and updated continually instead of every ten years.
http://www.genline.comThis is the specific page on Genline. (GID # = Genline Identification Number).
GID # 849.36.28300
The HFL covers the years 1886-1890 in Västra Torsås parish in Kronoberg län (county).
August Sjöberg, born 23? February 1850, married 30? December 1870
wife Ingjerd Persdotter, born 7 October 1851
s. Axel, born 10 February 1871, confirmed 1886, to North America 22 June? 1889, certificate # 45??
s. Per Algot, born 4 February 1878
s. Karl Julius, born 25 January 1881
d. Amalia, born 3 November 1883
s. Anders Henning, born 19 April 1886
s. Klaes? Henrik, born 7 June 1889
No birthplaces were listed, which is unusual at this time period, but the censuses help with that. Genline has birth records among all the other scanned handwritten parish records, so you can always check to make sure.
Judy