In rescue and in some shelters we keep a list of problem or be aware people and share the lists with other rescue groups across the US. The city pound should be made aware of this woman but I am not sure they will do anything unless abuse is reported. Their job is to move the animals through or euthanize them - per the law. I would be very surprised if the Humane Society is letting her do this as they keep records but to be on the safe side I would tell them also along with any rescue group you can find.
There have been small rescue groups that have made $$$ off of rescue and will not give shots or s/n the dogs. They use different people and different names to get their hands on these dogs and then will breed them or resell them. This is another reason animal shelters should be doing their own s/n instead of giving the people a refund IF they s/n down the road.
This whole situation is sad and hopefully you can help put a stop to it.