You'd see much faster results if took your existing internal filter and removed and wrung the sponges out in a small jug/container then dunk the sponges from your 2nd (newer filter) into the dirty water and leave it to soak for about an hour or two and then refit them back in the respective filter housings, this way you will distribute the nitrifying bacteria between the two and will colonise in the new sponges making it suitable for effective filtration. Just having another filter operating in the water will aid mechanical filtration but would take several weeks to establish any bacteria just from the tank water alone passing through it.