Adding filters does not create more bacteria, only more ammonia will do that.
The bacteria live in the greatest concentration where they can get the things they need delivered to them. A few bacteria are always motile, but for the most part they are attached to hard surfaces via a bio-film.
So, forget the idea of hooking the two filters together. This will do nothing to help with bacterial relocation and may cause issues. So what will work? Step one is to understand how to get bacteria out of the old filter and into the new one in light of the info above.
What you need to do is to make the old filter less hospitable to bacteria and the new one moreso. This can be done as follows.
1. Set-up the new filter one the tank with no connection to the old filter. Moving over old media with bacteria from the old to the new filter would be the most helpful. This is true even it it is only a bit of the media. If you cannot do this there is another way. Turn of the old filter and leave the new one running. Then rinse out the media from the old filter in the tank. The goal is for it to end up in the new filter. You can leave the old filter off for an hour to facilitate this process.
2. Make sure the new filter is running at its full flow rate. Slow the flow rate in the old filter without stopping it entirely. What you are trying to do is make the old filter less effective which will make the bacteria now inside the new filter re[produce faster. Over the next two weeks or so begin to remove some of the bio-media from the old filter which will result in the bacteria reproduce more in the new one.
3. A lot of the good bacteria in tanks is actually not in the filter. It is in the substrate, on plants, rocks and other decorations. Bear in mind that the bacteria is somewhat photophobic (it doesnt like light, especially bright light). So it will be in shaded or dark places in one's tank and filter. This is why filters are not made of clear materials.
Your filter is a good home for bacteria but is far from the only place iin a tank the bacteria are living.
4. The bacteria multiply faster when there is more ammonia/nitrite than they need. Conversely if these things are reduced, the bacteria will slow their reproduction. If the supply drops below what the colony needs to thrive, they will die faster than they reproduce and the colony size will shrink to be in balance with the lowered supply of ammonia/nitrite.
5. The bacteria in your old filter is not going to pack up and move to the new one. What will happen is a bit of the bacteria will get into the new filter and colonize. But it cannot go crazy because most of the ammonia is being used by the bacteria in the old filter. So what you are doing following the above plan is making the old filter increasingly less able to support the needed amount of bacteria while the new filter becomes a much better home for the bacteria.
6. Monitor ammonia levels during the changeover. Hopefully you will never see an ammonia reading during the changeover. But if you do, a water change will fix that.
7. Finally, bear in mind that, under optimal conditions that the ammonia bacteria can double in numbers in about 8 hours while the nitrite ones in a few hours more. The odds are very good that you can make the changeover and have no issues doing it.