MyPhoneExplorer without Google

According to …

… you could just copy it to the phone with the file explorer on the PC and then try to install it with a file explorer on the phone … which might need enabling Apps from unknown sources depending on your phone’s setup.
(Or did you mean PTP, which would be for photos only?)

Else, after …

… you could use the command line to install the APK with
adb install mpeclient.apk
assuming adb.exe is available from the path in which you operate the command line, and mpeclient.apk resides in the path in which you operate the command line, else you would have to give the full paths instead, e.g.
c:\wherever_adb.exe_is\adb install c:\wherever_mpeclient.apk_is\mpeclient.apk

See also here: Install APK via ADB Commands on Android Devices | DroidViews

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