Any incoming fish has to under go a full quarantine process no matter where they come from.
Most zoos/aquariums have set animal collection plans that are formed yearly. Animals are traded from other facilities, bought from acredited suppliers or collected from the wild with permits as a last resort. Only on rare occation will a facility look for a specific animal from the public. Point in case, the arapaima I picked up from a member here on MFK. It took three months of prep work, permits and a transport that was well over 36 hours of straight driving with a custom set up. Not something most places would do, but in our case, I wanted a sub adult fish and it happend to work out that the one tracked down needed both a larger home and needed to be moved out due to it's illegal status in the state we got it from.
Any offering of a fish would probably be over looked. I know of several places that have a fish donation hotline and instead of taking the fish in, will list off places that you can put the fish up for adoption instead. There are a lot of side things to consider when taking on a fish. It's background - by that I mean will taking this fish out of the pet trade reduce the number or just encourage more to be bought? How much money will it take to care for the animal- that needs to be budgeted for. Will it work in a current display? I know a lot of people think that any old fish can go in any old tank. Then on top of tank, there are certain collections that are actually managed by outside dictating forces - like breeding groups etc.... So the animal would have to fit in under those guidelines as well.
So the short version is that there is a lot that goes into adding at animal at a zoo or aquarium.