Quark XTension, ID2Q, can convert InDesign fonts to Quark. ID2Q can also convert several other Adobe InDesign elements to QuarkXPress. View this video on how easy it is to convert InDesign fonts to Quark:
If there are fonts reported as missing after a document conversion, try searching the Adobe application support folder, which holds several OpenType fonts that InDesign activates privately. On Mac, these fonts can be found in –> User/Library/Application Support/Adobe/Fonts
Get ID2Q, the InDesign to Quark XTension from Markzware that can convert InDesign fonts to Quark. ID2Q is available online via the ID2Q page. See more conversion software on the Markzware Products page.
Convert InDesign fonts to Quark with ID2Q, the Quark XTension by Markzware!