Correct me if I am wrong, but if you already have used filter media that is coming from a well established tank, then you do not have to do a fishless or fishy cycle.
Make sure your temp is the same and add the fish. Also, by removing the mollies from your 10 gallon, it will stop that tank from having a mini-cycle with different filter media.
I would move the filter media and the fish at the same time.
Just do a few extra water changes the first week.
I am new to testing water, but the way I was started was to do exactly above, I did not know it was called cycling at the time. It was what the LFS suggested. I just took filters from a running tank and moved them on a new tank and did 20% water changes every three days for about 2 weeks. I went from a 29 gal to a 55 gal, with no losses. 7 years later most of those convicts are alive. (1 died last July while the person house sitting unplugged the filter. We came home to a tank full of fish gasping for air. The convicts are back in the 29 and with the mother-inlaw. We gave them and the tank to her when we moved. Still all alive.)
From what I have read here this way of "cycling" allows one to put fish in the quickest.
If I am mistaken, please correct.