The FCL bridge allows you to move your tokens from Substrate to Gnosis and vice-versa, and also from Ethereum to Substrate or Gnosis. The first phase of the bridge will enable you to conduct your swaps via this website, and you can refer to this page to check how to use it.
This bridge operates with burn/mint functionality, which means there will be no additional supply. For example, the ‘native’ FCL tokens transferred over to Gnosis are going to be burned in Substrate before being minted in Gnosis.