She's the angry outsider. She can call the state fraud hotline and make a report. But that's as far as she can go. Her opinion of what "should" be done isn't worth a passing thought. And what they absolutely will not do is call her back and tell her what they did about the situation.
In some worlds, when people get mad at others the first move they are going to make is calling the department of social services and reporting them for food stamp or other assistance fraud. Happens all the time.
And they'll investigate. But there's really no way this person who's so concerned with the protection of her taxpayer money even knows exactly what kind of "welfare" the other woman is receiving. She also has no idea what is being submitted on her information checks or what address she is using.
As for the other person being prosecuted for helping the woman commit this welfare fraud, that's a pretty big stretch. Since the actual dollar amount of fraud being committed, the amount of resources being expended in this (even if she's a blatant fraud case) are going to be really small, there probably will be only sanctions against her, no prosecution of the case. In other words, it's not worth tying up the court system, not worth building all the jails necessary to hold every single person who does things like this. Not to mention prosecuting the person who's supposedly enabling the supposed fraud. How much court and investigator time would this take up?
Hey, bank and company CEO's defraud the taxpayers of billions of dollars all the time, how many of them get prosecuted?