As Kevin said, it's rather simple. If you are using the same filter just move it across when you move the fish and move as much water as possible. This means your fish only see it as a large water change and you don't need to cycle the filter again.
If you are using a new filter on the big tank, either run both filters for a few months and then see if the tank can survive by taking out the old one. A better method is to take all the rings, sponges and other media from the old filter and squish it into the new one and then just run that one. This method also means you don't need to cycle the new filter.
After a move just keep an eye on the water stats (ammonia and nitrite) for a week or so.