Hi Jonty,
The idea of a mature media transfer is just to get a nice bit of biomedia that has the beneficial autotrophic bacteria growing all over it from one filter to the other, as you say, and to just make it happen mechanically any way you can figure out without blocking the flow in the new filter or losing too much bacteria from the old filter.
One guideline to be aware of from the start is to not take more than 1/3 of the biomedia from the old filter. That should assure the old filter continuing along without a mini-cycle interrupting its effective operation. If the mature filter has "lose" media, like ceramic rings, ceramic gravel or bioballs, then its relatively straightforward figuring out a reasonable amount and figuring out a place to stash/cram it in the new one. If the mature filter has sponge media, especially sponges that are "shaped" to fit tightly, then its a little more involved in that you'll want to perhaps purchase a fresh replacement filter for the mature one and then get ready with some scissors. Take a look inside the new one and figure out where you're going to be able to place the media and thus what shape will work most easily. Then go back to your mature filter and plan a scissor cut that is matching on both the old gunky filter sponge and the dry new one. Make the cuts. Tranfer the mature piece of sponge to the new filter and fit the new dry piece of sponge tighly into the vacated spot in the mature filter.
Hopefully this gives you the idea. In practice it will probably be up to you to be creative. Just be sure to try and get a healthy bit of mature media moved over and of course keep it wet during the transfer process. The ease or difficulty in this process often is such that it is one of the events that enlightens beginners about why large external cannister filters are so loved by experienced aquarists. Having big easily removable trays that are just open and not particularly designed to limit the type of media you can use is a godsend when you want to do mature media transfers or other odd customizations of your filter media. Its just an extremely flexible sort of arrangement. Personally I think eheim are that masters at this sort of design - everything very, very simple but very tight, not allowing leak paths in the water flow through the filter but allowing maximum flexibility of tray manipulation and tray use.
Good luck with your MM transfer!
~~waterdrop~~
