First of all, we confirm that you can export your project created in Movavi Video Editor or Movavi Video Editor Plus if you purchase Movavi Video Suite as the latter includes Movavi Video Editor Plus as editing module.
Also, any newer version of Video Editor or Video Suite should open any projects made with previous versions (but not vice versa).
While the projects made in other versions/products will not be shown in Recent projects, you can still open them manually via File menu -> Open Project.
In order to export your project in Movavi Video Suite, please launch the program and open Edit video module.
Then, please go to File menu -> Open Project and find your project on the computer.
Please note that by default projects of Movavi Video Editor are stored in
C:\Users\%username%\Videos\Movavi Video Editor\Projects
If the issue with your project still arises, please contact us so that we could investigate the issue further.