The best, and most reliable way of going about it is to take
all the media from your internal and put it in the external, then fill in the gaps with new media.
If you just run the two filters in tandem, there is little incentive for the bacteria to colonise the new filter, as the old one will be dealing with all the fish's wastes already. Also, because the bacteria cling onto the media quite strongly, there won't be enough loose in the water to even get into the new filter.
Another advantage of doing it that way is that your old media stays cycled, so if you ever need to set up a quarantine or hospital tank in a hurry, you can just take the old media back out of the external, pop it back in the internal, and you have a cycled filter ready to go any time you need it
Of course, you could run the two filters in tandem, but you should still 'seed' the new filter with some old media, and you'd have to run both filters for at least six to eight weeks to build up enough bacteria in the new filter for you to able to remove the old one.