The recent builds of memoQ 6 have caused some confusion with Kilgray following the SDL practice of creating its own extension for XLIFF files, so these may not be recognized by other applications and would need the extensions changed to XLF or something else generally recognizable as XLIFF.
This can actually be done directly in the export dialog for the bilingual XLIFF file. Just change the file extension in the File name field. Despite a renamed extension, the file will be recognized as a memoQ bilingual when re-imported, and the translation of the original file will be updated.
If you encounter a compressed memoQ XLIFF export (MQXLZ), be aware that this is just a ZIP file. Rename the extension to ZIP and unpack it to get the real XLIFF (MQXLIFF) file. That file has a generic name (document.mqxliff) and should probably be renamed before it is shared.
Update 2013-07-23: Here is a short video I posted on YouTube to show how to export an XLF file and open it in SDL Trados Studio: