Going from Starter Membership to Extended Theme License
You can continue to use the theme as-is. All theme files in the package (regardless of membership or lifetime support license) are identical.
The only difference in download is if the theme is not entirely CSS-based. Then you'd also have a PSD in your download package. Mobius is purely CSS-based so all the customization options are in the control panel for the most part.
With the extended license, you'll always be able to login for support, download the latest version (for any new projects), as well as receive updates to existing installations.