I'm trying to use "Simple Fracture" tool simulate crushing a fracture object (sphere) with a collision object (box).
I kind of achieved that by setting the "Bullet Data" of the box to "Active" in "RBD configure". However, only the collider is simulated, the box object will stay in place.

Is there a way that I can get the box to move along with the collider?

The collision input on the RBD Bullet Solver is there for convenience when you want to input colliders that you don't necessarily need to retrieve from the sim - i.e: static environments, animated characters you want to interact with your RBDs, etc.

If your cube is a hero RBD object however, merge it with the fractured sphere so you can feed it into the RBD Bullet Solver's main inputs. You'll want to ensure it has a name that doesn't clash with the sphere pieces' names. If the sphere has both render geometry and proxy geometry, you need to make sure the cube does too - you can use the same geometry for both.

You can either do straight merges or use the RBD Pack, Merge and RBD Unpack - the latter might make it easier to work with triple wires, and it does have an option to ensure names are unique.

Thank you very much!
It's working perfectly.