I would definitely not try to use he semi-mature filter until the ammonia levels in the new tank were at zero. All filters need cleaning once in a while and why not do that cleaning in the new tank is all that I really would suggest. By doing it there, oyu will seed the new filter with some of the bacteria from the existing filter and hurry the fishless cycling along. I would think it was a better use of those bacteria than putting them on the garden with removed tank water.