Yes, any copper wire will do. As Mattylad suggested, you can use the cut-off legs of resistors if you have any. Obviously, the wire has to be solderable to connect it to the board again so tinned copper wire would be best. The black coating on the broken parts is just epoxy resin to stop the ferrite beads rattling if you shake the machine!
Their purpose is to stop unwanted signal leakage in or out of the socket and the cable plugged into it. Often they are needed so the machine passes the strict EMC regulations that set the limit for how much interference it is allowed to radiate. They also form an electrical bridge across a section of the board which may be used to allow copper traces to run underneath it. If you are confident nothing will be upset by interference leakage (buzz and whistles on nearby AM radio for example) you can just link a wire across without fitting the beads at all. It may break the regulations but speaking practically, the level of interference is likely to be extremely low and despite bearing conformity labels, quite a lot of other equipment never meets specification from new.
Brian.