If the socket is detached from the logic board there are two ways to restore the connection from the inverter cable to the board. NB: it's almost impossible to resolder the socket to the logic board if you don't have the machine to reflow the socket but you can:
1- solder a wire from each contact point on the logic board to its specific location on the socket
or
2- cut the inverter black connector from the inverter cable and solder the six cables directly to the contact points on the logic board.
You need a solder iron with a fine tip to do this job. Dont put solder on the contact points but only a small amount on the wire end then place the wire on the contact point, apply a scotch tape on the wire to keep it directly on the solder point then briefly touch the wire end with the solder iron tip until the solder melt. Be careful, don't bridge the contact points with solder cause you'd short the board. Once the solder job is done, test the iBook lightning system. If it's working ok then apply hot glue on the solder job to secure the wires on the motherboard.
Warning: this is a skilled tech job. If you do a mistake you can easily destroy your logic board.