Affiinity Designer supports document export to Adobe Illustrator's AI format and thus can be used for AFDESIGN to AI conversion. Seems there is no other way how to perform this conversion as *.afdesign files can only be opened in Affinity Designer.
Convert Serif Affinity Designer document to Adobe Illustrator graphics file.
We found one software available in the database for this conversion.
Apple macOS / Mac OS X software - convert afdesign to ai on OS X
Professional graphic design software for the Mac
Convert from afdesign file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.