How many fish (and what size) are in the current tank? If you put media from the established filter into the new one, you should be able to add the fish immediately.
Remember, bacteria grow slowly in a filter to match the bioload of the tank. If you have a tank say, with 30 fish, and you then use that filter on a new tank with only 10 fish in it, of a similar size, some of the bacteria will die off. So, how much of the filter media you use from the established filter will depend on the bioload of the 2 tanks.