Wash the cabbage head, and then cut into quarters and remove the core
Slice thin and then cut the slices into halves or thirds
Sprinkle with vinegar, set aside

Melt the butter in a large saucepan, add the sugar and salt
Add the cabbage/vinegar combination and cook 15 minutes, stirring regularly

Add the lingonberry preserves and mix in well.
Turn to lowest heat and gently simmer uncovered for about 90 minutes, stirring occassionally and then more regularly as the moisture evaporates. (This step may take up to two hours, depending on the cabbage moisture content.)

Watch carefully the last half hour to make sure it doesn't stick.
When the moisture is cooked off, remove from the heat and serve or cool until ready to serve.