If I were you, I would take this to a professional- this is a quick fix if you have the right equipment and know how to do it safely. If that is plastic surrounding the cup, definitely refrain from soldering it yourself. If you want to go ahead and do it yourself, my best advice would be to research the charger- you will be less likely to damage it when you solder. See if you can find schematics, materials used, temperature ratings etc. Don't solder electronics with an iron without temperature control. As others said here, use flux!!! It's crucial for making a safe connection- figure out if you're using leaded or lead free solder and buy a syringe of the appropriate flux for it. Apply the flux to the joint and melt it with your iron. Melt some solder into the cup, and then heat the solder while lowering the wire in. The less time you have the iron in contact, the better your chances are, but make sure not to apply too little heat. Use 90% rubbing alcohol and a brush to clean the joint after.