Add ground earth to a Chinese music player
There is no way to fix this. Look at the picture: The mains input goes onto the PCB without any means of isolation. There is no transformer, and there doesn't even appear to be any cheapo alternative that might, probably, be acceptable - like two safety rated capacitors that might allow charging the batteries while maintaining isolation. Those capacitors would have to be very small in value because otherwise, they would allow a significant (read: dangerous) current to earth.

If you were to introduce an earth connection, it would, at best, cause your fuse to blow. At worst, the earth current would set stuff on fire.

Having no earth wire, it would have to be a class II device. This means that the entire circuit must be isolated to the user in a proper (double/reinforced) way. This is not happening here (antenna, battery compartment may be accessed, pushbuttons, headphone outlet, speakers, ... pretty much anything on this f-iretr-ucking piece of lethal junk.

Also, there is no way the two little black wires coming from the input connector are rated for mains voltage levels. They may cause a short between the two input contacts, causing a fire.

This device is a death trap, and it has taken the idea of making stuff cheap way, way, way too far. Return it to the dealers. Tell them you're serious about putting them out of business if they don't stop selling such warez, immediately.