BetterSnapTool doesn't work in Mojave v10.14

This is caused by a bug in macOS Mojave. Sometimes the Apple tcc.db gets corrupted.

First you can try this command and see whether it is able to reset your tcc.db, however most of the time when it is really corrupted that doesn't work:
sudo tccutil reset Accessibility

You can try to run "first aid" in the Apple Disk Utility. Sometimes this will fix such issues.

If that also doesn't help, the only solution is to delete the TCC.db file, however that's complicated because it's protected by SIP.

The (advanced and complicated) steps to delete that corrupted file would be:
0.) Boot into recovery mode
1.) Disable SIP (system integrity protection). Which is a complicated process unfortunately ( https://apple.stackexchange.com/a/208481 )
2.) Delete the tcc.db file (e.g. using this command: sudo rm /Library/Application\ Support/com.apple.TCC/TCC.db )
3.) Enable system integrity protection again (command: csrutil enable )
4.) Reboot the Mac