I don't know if this helps at all with Designer but I did a review on Facebook of the best ways to get FreeHand files into Illustrator CC; especially with live text intact. Sometimes PDFs work but a third-party plugin was best.
If there is some way to harness this for AD, that would be great as FreeHand file import is a mess unless it is a very simplified file.
Using gradations and text, here's what happened when exporting from FreeHand in different formats:
1) Exporting a FH file to Illustrator 7 format will have editable text on a path but the type will shift position. Gradients will breakup into bands with noticeable borders. Blends work the best.
2) Exporting a FH file to PDF and opening into AI will have smooth Gradients and Blends, but text will breakup to individual letters and the text path is deleted. PDF's work best if there is no text in your FreeHand file.
3) Using native FH file and opening with Tensai AI Plugin in Illustrator will have accurate gradations and blends. However, text brackets on the path are collapsed on import. Expand the brackets and your editable text will appear.
If you have a FreeHand file with no text, create a PDF and open in the latest AI. If you have text, use the plugin.
When exporting TRANSPARENCY effects from FreeHand to Illustrator in different formats: (see below)
1) Original FreeHand file with Lens effect and transparency. This is how it looks in FHMX:
2) Exporting the FreeHand file to PDF and opening the PDF in Illustrator will divide the transparent sections into blocks. It also removes all actual transparency and 0% areas revert to the white background.
3) Using native FH file and opening with Tensai AI Plugins in Illustrator will keep the transparent effect intact. You can move the elements around and still have transparency.
4) Exporting a FH file to Illustrator 7 will will not work at all; it deletes the overlapping elements. (no image shown)
Bottom line is if you have one or two FH files to convert over to Illustrator, exporting your file to PDF works in most cases. If you have more complex files, or a large number of files, get the Tensai AI Plugin