Just re-solder it back on. Looks like there may even be enough solder left there for you to use the soldering iron alone and reattach. If your uncle doesn't have one just buy a $5 one at menards or walmart. Basically you would just hold the wire that fell off over the broken connection and heat it up with the soldering iron(Once the iron is warmed up. Can take around 3-5 minutes). Once you see the solder liquify which should be fast then take the soldering iron away. Should cool/harden in 5 seconds.
You can then probably just clear epoxy the jack itself in place so it won't push in again. Even though most epoxy hardens in 5 minutes. I'd wait a good hour before trying to plug anything into it.