When cloning mature media from an established filter to a new filter you should always treat it just like a fishless cycle if possible but be hopeful that it might be as quick as a week if the media transfer "takes." Most of the time it "takes" just fine but occasionally the transfer will just cause the bacteria to be shocked and shut down or die.
So this means you need a liquid-reagent based test kit (which you probably already have as an established fishkeeper.) And you'll need to pick up some household ammonia if you don't already have some. Members can advise good brands/sources depending on your location.
When you move the MM you don't want to take more than 1/3, so that the old filter won't suffer a mini-cycle. In the new filter you should try to position it so that is right before the main biomedia in the water path or is right beside it in the same tray. Its better to cut some space in a new sponge rather than squeeze the sponges so tight that water movement is inhibited. Then, after all that cutting and fitting, the final step is to clean the rest of the established filter media directly in the water of the new tank. This will be sucked in to the new filter and give it an additional boost. Run your temperature at 84F/29C and take pH and nitrite readings along with ammonia of course.
If you've forgotten the fishless cycling technique, re-read it in RDDs article in the BRC and look for the Add&Wait method. I'll bet your clone will be able to drop 5ppm of ammonia to zero ppm ammonia and nitrite within a week or so if the old filter is fully mature. Once it shows it can drop it to double-zeros for a week, do a full water change, adjust temp and move the fish.
~~waterdrop~~