To remove the cartridge reader look for 4 solder joints, 2 on each side of the reader (see image).

Apply heat to them with a soldering iron to melt the solder and take out the reader. Use a spludger to lift the reader out of the board as you apply heat.

You can apply some solder flux or even some new solder wire to form an alloy between the old and new metals, this would ease the task.