Although there is not a direct way to save a separated AVA file as .ai to open in Illustrator, there are some steps in the embedded video here you can follow in AVA and Illustrator to achieve a similar result in both programs.
The multiply transparency will simulate a generic RGB overprint of design information only. Specific overprints in AVA such as reflectance 3 may deliver different results.
Exporting of colours from ColourSys as ASE format may differ from original design colours.
Results may vary with some design types, especially those with more overprint coverage.
© Design used copyright to AVA CADCAM Group Limited 2016.