On Android 5.0 and higher, in order to access the external data storage on the phone (i.e. SD card) you can use the Document Providers function. Select Document Providers in the main menu and then click on "Select external storage".
Upon clicking on that, the following message will be shown and the following screen will appear on your phone.
On the phone, click on the menu and select the desired external storage and then tap on "SELECT" in the bottom right corner.
After that is done, MOBILedit will automatically re-read the files and you will be able to view them on your PC. Please note that the external storage will be named by 8 letters long code name (thats how the phone calls it) as shown below.