To release the cartridge reader look for 4 solder points, 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.

CAUTION: Soldering iron can cause severe burns if not used properly, proceed with caution and have an adult in the room with you if underage.