It has never existed a Jönköping socken so you are right this posting is strange.
That's not correct. In the old days the town Jönköping only had one parish, called - Jönköping. Then in the year 1600 a new parish was founded, called Jönköpings slottsförsamling (slott = castle), but the real town parish was still called just Jönköping.
This did not change before 1852, when the parishes were renamed: Jönköping -> Jönköpings Östra (East), and Jönköpings slottsförsamling -> Jönköpings Västra (West).
Then in 1921 the names were changed again (officially, but the new names were used unofficially before that): Jönköpings Östra -> Jönköpings Kristina, and Jönköpings Västra -> Jönköpings Sofia.
Jönköping is the centre of a county (län), named after its 'capital'. But the county is not called just "Jönköping", it's called "Jönköpings län". If you say just "Jönköping" you're talking about the city.
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Maja Stina is moving to Östenstorp in 1834. It's page 21 in the same book (Frinnaryd AI:5).