How long has existing tank been established? If it's been a while (2 months or more) there is probably more than enough bacteria on the decor in the established tank to put a brand new filter in and not miss a beat. I wouldn't worry about putting old water in new tank. Most of the bacteria you want is going to be growing in filter or filter media and rocks and decor that's been in older tank for a while, the water itself doesn't really have that much benefit. Not sure what type of filter you have but for example I have a 60g established tank with an HOB filter and I also have two sponge filters in there as well just in case I need to set up a tank quickly. I have actually taken the hob filter off walked it over to new tank just filled with tap water and "prime" conditioner, heater, etc and plugged it in and never had a problem. Same with sponges I just pull them out put in new tank and your good. Plus if your just moving one shrimp the bioload won't need a ton of bacteria to handle the waste.