Dangling the filter or media in won't really help, no, lol. But any piece of actual media (sponges or ceramic rings or whatever you've got in there) will do the job.
If you're getting a new filter, then take the old, smaller one apart and split the media between the two tanks; some to seed the old tank's new filter and some for the new tank, and then split the fish accordingly.
So if half the media stays in the old tank (in the new filter) and half goes into the filter in the new tank, then you should put half the fish into the new tank and leave half of them in the old tank.
Or if you put just 1/3 of the old media into the new tank, then move a 1/3 of the fish too.
Hope that makes sense!