You didn't say when Axel Edvin was born but this man emigrated in the same general time period as yours, although slightly later. Perhaps he is yours but how can I tell without knowing when yours was born?
Emibas was made from registrations in the Swedish parish to go to a foreign country. It is about 75% complete. Hopefully you know his occupation and birth date.
Svensson Rosenqvist, Axel Edvin Skomakare = shoemaker. (unmarried man)
b. 6/23/1861 in Nässjö, Jönköpings län (Småland)
Emigrated 10/26/1882 from Gamlarp, Nässjö, Jönköpings län (Småland) to Nordamerika
Source: Household Examination Roll, p. 57
Emibas migration file ID: Nässjö F 1882 031
Emihamn was made from registrations with Swedish port police before leaving Sweden. (Not all Swedes left through a Swedish port.)
I hope you also know some locations where he was known to live.
First name: JOHAN Last name: ROSENQVIST Age: 21Gender: M Parish: NÄSSJÖCounty: F (Jönköping) Port: GÖTEBORG Date: 1882 11 10 (November 10) Destination: ROUND ROCK Fellows: NEJ Source: 21:678:30018
There are handwritten Swedish parish records online which you can see if you join Genline, a fee-based service. Parish records are the main source of genealogical information in Swedish genealogy.
I checked to try to find the birth record for Axel Edvin and I think the date provided on Emibas is incorrect. (Dates are written as numbers in these records and a misreading of a number in a date can result in incorrect birthdates, etc. This record is more likely to be correct, but it is an extraction made in 1861 from the full birth record (not online at Genline), so you need to see that too.
This is the specific page on Genline which has this birth record.
parents: Johannisson S. (must be Sven, since he was listed as Svensson Rosenqvist on Emibas; Axel Edvin probably took the name Rosenqvist when he became a shoemaker.), Br. (Brukare = user, most likely of a farm, in Träslända (a village in Nässjö parish) and Jonasdotter, M.L., wife.
mark in column for married parents.
43 (age of the mother)
I see listings of three Texas locations with access to Genline.
Many of us find useful information using the Swenson Swedish Immigration Research Center. They have a website but their extensive collection of records is NOT online. We need to go there to research or pay them to research for us. They have records which are difficult or even impossible to find elsewhere.