Charcoal in a filter really is only effective for 2-4 weeks. After that, it stops doing the things the carbon does, and it just becomes another place for bacteria to grow.
You can either just leave the charcoal in since after a while it won't do anything charcoaly anyways or you can add in a piece of aquarium sponge along with it and then wait a few weeks then remove the charcoal cartridge. Bacteria are always interested in living in the most favorable place with the least competition for food, so enough bacteria will spread out migrate to the sponge that you should be safe removing the other cartridge after a while.
You can either just leave the charcoal in since after a while it won't do anything charcoaly anyways or you can add in a piece of aquarium sponge along with it and then wait a few weeks then remove the charcoal cartridge. Bacteria are always interested in living in the most favorable place with the least competition for food, so enough bacteria will spread out migrate to the sponge that you should be safe removing the other cartridge after a while.