I maybe wrong but the only thing that looks like a way of exporting the ArchiCAD Properties is to manually go through the IFC Translator mapping settings and add the Property to each type of IFC Element.
It's taken an hour and half so to do. I was hoping there was a nice button that would do it for me
AC versions 3.41 to 25 (UKI Full 5005).
Using AC25 5005 UKI FULL
Mac OSX 10.15.7 (19G2021) Mac Pro-2013 32gbRam AMD FirePro D500 3072 MB graphics