Moving along to the 6th century until the 11th. Some of the Germanic tribes, Angles, Jutes and Saxons (but not the Franks), decided to conquer the eastern British Isles. In this move they subjugated those the British Celts (Bretons, Iceni and more) and thus created the English speaking Kingdom. These groups of people overtime became Anglo-Saxons. By the 10th century, the early foundations of the Danish, Norwegian (Norway), and Swedish nations began changing their pagan (nature beliefs) beliefs to the spread of Christianity (man made beliefs). They were all to converted by the 12th century.
The Norsemen spoke Old Norse, which they even called dönsk tunga (the Danish tongue) not German. If you are interested in this stuff, please direct your attention to a wonderful URL – http://euroheritage.net/eddaintro.shtml. Here you can see clearly the mix of Celts and Viking cultures. Now that we have that settled, lets get on to the 'claiming of the Runes;
Runes who claims to have Invented them?
Now during the period from 550-750 AD, rapid linguistic changes occurred, as it seems there was a split in the Danes related to Swedish tribes. Some went south and west. During this time their language was no barrier in communicating with tribes across the lands; from Greenland to the Baltic, nearly the same language was spoken throughout, yet each tribe's homeland could be identified by his accent. Then a significant difference changed between the Norse (Sweden and Denmark) and West tribes (Norway and the Atlantic settlements such as Iceland).
The Norse might be the people who created the Runic Alphabet but no one knows for sure. Obviously one man in a tribe created them but which area they actually came from. We will NEVER know. We do know that Runes were used for centuries since Christianity became popular in about the 500's, especially in the Sweden area.
The evidence of the runes symbols origin is forever shrouded in mystery. Having read above, and now knowing that no one is of pure race, no one can really 'claim' them. But we do know, obviously, that the inventor was a Priest like person whose creativity was inspired by the Divine Gods and their lessons of scholarly coded poetry, learning different metres and kinds that we see in the Eddas.