A license purchased for Mac cannot be used for Windows or Linux versions and vice versa for all platforms.
If you purchased an app from the Mac App Store, delete the trial version and download it again from the Mac App Store (direct access from your list of purchases).

For security and privacy reasons, you need to connect to your account to see your licenses or you can receive your licenses per email.

Get licenses per email
Email used for the purchase:

You can login/register with your Apple ID or with your xProline account

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