You can play / progress your Summoners War Chronicles (SWC) game both on PC and on your mobile and you can this easily. All you have to do is log in to your PC and follow the next steps to sync your game to other platforms.
Account synchronization on the PC version
It is important to synchronize your account on the PC version to continue your progress in the game. Here are the available connection methods:
If you log in with the account you use on your mobile device, you will be able to play on the PC version with the character you were playing on your OS or iOS device. You can check the synchronized account in Settings - Account - Account Synchronization.
By synchronizing your account, you can of course obtain rewards that will allow you to obtain resources to perform summons and obtain powerful monsters.