Thanks for all the replies guys, I really appreciate it, I think all of them are great advices worth trying, I have a feeling that win32's method would work best but I want to try all of them 1 by 1.
I will first check if RainyShadow's advice is possible, this "USB storage" option - does it show only when I connect the phone to the PC or I can find it in my phone Settings?
My phone model is: Samsung Galaxy S5, SM-G900V, Android 6.0.1, 5.1" 1920x1080 screen, 16MP camera, 2GB RAM.