You may have to search places like this to find a socket that will physically fit into the space and has the same pcb connection configuration. (I'm assuming that it is a TRS type socket -i.e. 3 rings on the audio plug).
I thought that you meant that the internals of the socket itself were broken. See blue arrow in image
(click on image to enlarge for better viewing).
If that is so you'll have to unscrew the pcb from the case onto which the socket is mounted and unsolder the socket from the pcb. Then you'll have to determine the connections between the socket and the pcb so that it matches the wiring going away to the headphones.
Usually with stereo audio socket and plug, the tip contact is the left speaker, the ring contact is the right speaker and the sleeve is the common earth for both speakers.
If the headphones have a microphone (don't know the headphones myself) then you'll need a TRRS socket instead.
Same convention although it may be tricky with regards the microphone connection in the socket. Does the cable plug have 3 or 4 rings?
See if you can ascertain the board number on the socket board, check both sides of the board (can't quite make it out myself, - old eyes ;-)
If you can make out a board number Google search the number only and see if there are any results. Worth a shot.