I'm sorry. I can't help with research in Texas, although I'm aware of a book about Swedes in Texas. That might even be the name of the book and I think I've heard that parts of the book are online. The Swenson Swedish Immigration Research Center has some microfilmed church records for churches in Texas but those are not online. The address for the Swenson Center is in a link I provided in my first message. Also check their microfilmed Swedish American newspapers. Those can be ordered through interlibrary loan.
Even though you probably know the following, I had already found this and I might as well put it here, just in case someone else needs it in the future.
The birth parish (Hasslöv in Halland county) for Albertina listed on Emibas is incorrect. The transcriber must have misread that parish. When I checked the birth in Hässle parish in Skaraborg county, I found her birth. (The household exam had said she was born in Hässled, which is the old spelling for Hässle. I learned that by researching one ancestor who was born in that parish.)
Swedes love to confuse us by changing names and this family is no exception. The father was a husar (hussar; light cavalryman) at the time of her birth and he had a military name. He must have changed that military name. Swedes LOVE to change names. (A Swede told me the word 'love' was not strong enough and told me to use 'LOVE'.)
Read that Swede's article about Swedish naming customs.
At any rate, her handwritten birth record can be seen on this page from Genline.
637.25.110500,[Skaraborg]Hassle,C:5, Births,Deaths, 1800 - 1860, 0/263,Image 139 of 176
Albertina was born 18 October and baptised 21 October 1849 in Hässle parish in Skaraborg county. Her parents were the husar Johan Öster??? and his wife, Inga Broman. The mother was 36 years old. They lived in H something torp in that parish. One baptism witness (Usually there are several, so this is odd) is mentioned. He was Gustaf Vallström with H.H.???? torp.
I had looked in your old posts and found that you were seeking a Gustaf Björkander. I found one on the Emibas CD who was born in Skaraborg county and what really caught my attention was that his title/occupation was stationskarl. (Remember that the father of Albertina had that title in the record found at the time she emigrated from Sweden.)
Björkander, Gustaf Stationskarl (unmarried man)
b. 6/1/1845 in Skaraborgs län (Västergötland)
Emigrated 10/13/1882 from Stadsgården 8 Stora Glasbruksgatan 7, Katarina, Stockholms stad (Uppland) to Amerika
Source: Rotemansarkivet, häfte 13912, s. 12
He left from Katarina parish in the city of Stockholm. The Söder CD covers part of that city and it listed his birthplace as Hässled (the old spelling for Hässle) in Skaraborg county.
I guess you don't need a check to see if he had the same parents, since you already know the Swedish information.
I hope someone can help you with the information you need.