MXLIFFs are primarily intended for translation inside the CAT editor or to be directly imported via the UI and can be downloaded from the editor from the menu if download access of MXLIFF files is not restricted by a project manager.
Once finished processing in Desktop Editor or other tools, MXLIFF files can be imported via Tools > Upload.... Multiple or large MXLIFF files may be imported in a single ZIP file for convenience and a quicker upload.
When translating MXLIFF files outside of Phrase, it cannot be guaranteed how the files will be processed by other software.
MXLIFF files are not automatically recognized by SDL Trados and are only imported as reference documents. To import an MXLIFF file into SDL Trados as a translatable file, the extension must be changed to XLIFF.
SDL Trados adds additional information to XLIFFs that are not a native part of the MXLIFF file format. Select the Preserve; don't add if not originally present BOM option and the Do not store segmentation information in the translated file setting when exporting from SDL Trados to produce a file that be used with Phrase.
See Marek Pawelec's blog post for current instructions.