Some large file and network operations can take a fair amount of time to complete. You do not need to wait for such operations to finish before you can continue using FX or other applications on your phone.
If you begin an operation which will take some time, just tap the "Close" button on its progress dialog. The operation will continue in the background.
Active operations will be visible in the Android status bar. You can additionally see very detailed information about active, completed, and failed operations by tapping the "Window" menu and selecting "Operations". From this "Operation Manager" screen you can also cancel ongoing background operations if desired.
You can press the sleep button on your phone/device to turn off the display while active file transfer operations are occurring. The appropriate networking systems of your phone/device will continue to operate until the transfers have completed. Be aware that like anything else you do with your phone/device, long running transfer will of course consume some battery life.