Although there is not a direct way to save a separated AVA file as .ai to open into 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.

The 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