> The umlaut symbol originated in German but has been borrowed into other languages, including Swedish
Actually, no. In Swedish, Ä is not an A with an umlaut, Ä is a distinct letter of the Swedish alphabet. Swedish has nine vowels: AOUÅEIYÄÖ, unlike German, which has five vowels: AEIOU, and three umlauts: ÄÖÜ.
The evolution of it in Swedish comes from Æ -> Aͤ -> Ä, while in neighbouring Denmark and Norway, they kept both Æ and Ø. All three languages also have Å, which comes from AA.
Super-mega-pedantry edit:
Okay, the article says Swedish borrowed the umlaut symbol, and this is actually true. In the 1500's when printing presses were becoming common, Swedish printers imported them from Germany, the German ones didn't have Æ types, but they did have Ä types, and the Swedish printers essentially went "ah, fuck it, can't be arsed", and started using Ä and Ö.
...while the Danish printers also imported the presses from Germany, but said "fuck you, we're making our own types" and kept using Æ and Ø.