the Mate ubuntu should be able to pickup MTP when gvfs-backend is installed
Settings → Connected Devices → USB → File Transfer (de: Einstellungen → Verbundene Geräte → USB → Dateiübertragung)
and then just mount the device in the file browser.
Other options for cable are plain adb pull or adb push. For simple networked file transfer there’s localsend, for continually syncing (involving a bit of setup) syncthing is alright.