This would have been far easier if you had done it before the mail disappeared. Drag and drop is preferable to this.

Rename the mozbackup file to have a ZIP extension. drill down into the folders in the zip file until you locate the IMAPmail folder. Open the folder for your IMAP server Extract this folder and it's sub folder to a new location using a zip program or drag and drop (Note the location you placed these files in as you will need to find it again.) Install the import export tools add-on. select a folder in Local folders to add this mail to. then use the entry on the bottom of the tools menu to import an mbox file. In the dialog select the last option and then point the file picker to the server folder you created earlier. Allow the tool to search for and import whatever MBOX files it finds.