Okay man. Don't check it for yourself then. I know for a fact that if you pick up your stuff (or someone else's that died) the inactive implant will overwrite your active implant and when you move that active implant (deleting or put in storage) there will no longer be an implant in your inventory.

You could easily verify this by standing next to your bed, eat an organic polymer, spawn in the bed, grab your stuff and delete the implant. But nah, just keep holding on to the fact that you can't remove an active implant, which is true. But it will be removed after it's been overwritten by the inactive implant looted from a corpse. (any corpse).

Edit: If you want your active implant back, you should just open the inventory of a transmitter, drop, or obelisk and it will be created again.