What happens when you click on a MP3 track? There's no need to transfer anything because it plays MP3 as a default. It won't play a .WAV file. Just what are you looking to do? Clicking on Music will show tracks whether they are on the file system or teh SdCard.
Connect the phone and mp3 player to a PC and transfer the files. That will work for sure.
If you can find the cables and adapters to be able to connect the mp3 player to the usb on your phone it might show as an external drive but I can't say for sure.
You can try getting an OTG USB cable (with microUSB on one end plugging into the phone, and female USB-A at the other where to plug the MP3 player), and use some file manager on your phone to copy the tracks around.