Your game progress is permanently connected to the platform where it was created. Transferring your account to another platform is impossible since all game versions use their dedicated servers.
For example, if you create a game account on Facebook, it's permanently linked to Facebook. You cannot access it on hero-wars.com.
Hero Wars Universe has two separate games:
Hero Wars: Dominion Era (for PC and laptop browsers)
Hero Wars: Alliance (for mobile devices)
Hero Wars: Alliance is developed by a separate team and has different game mechanics, so there is no progress synchronization between the two games. If you have an account in Hero Wars: Dominion Era and download Hero Wars: Alliance, you will start a new account.
You can still launch Hero Wars: Dominion Era on a mobile device. However, stable performance is not guaranteed for now. The developers are working on optimizing the game for mobile browsers. But currently, the best way to play Hero Wars: Dominion Era is on a PC or laptop.