Rodders, adding water from an established tank is not useless, but it really does not accomplish much. An overwhelming percentage of the bacteria are sessile, not mobile, and living in the biofilm that is on all the surfaces in the tank. Just taking water, you would only get that very very very rare bacteria that is mobile. That is why it is usually suggested to take substrate or decorations or live plants because those will have the biofilm on them. Also, unless the other tank is densely planted, there is probably nitrates in the established tank water and when the new bacterial colony starts its work, addiitonal nitrates will appear and those may reach a very high level.
Ass rdd suggested, you could purchase the new filter and just run it in the established tank. In about 7 to 10 days, it will have a significant amount of bacteria, but not quite enough for a fully stocked tank. You will have to add (transfer) somewhat slowly and monitor the water parameters. You will be able to go faster than cycling with fish, but not quite a full stock.