App Store doesn't recognize my purchased Final Cut Pro app

In February, my logic board was replaced, and the App Store sees my laptop as a new computer, so it's no longer recognizing some (but not all) of my purchased apps. I purchased Final Cut Pro via the App Store in December. The installed version runs fine, but the App Store won't update it to the latest version (10.2). The "Buy" button in the App Store says "Install," but when I get an error message that reads "Final Cut is already installed on this computer. Choose Software Update from the Apple menu to check for available updates." But there isn't a Software Update command in the Apple Menu anymore -- just a link back to the App Store, which won't help me! How do I get the App Store to let me install the new version?