In my research, only about 800 such lawsuits are filed each year. Only about 25% win. The typical win is for millions of dollars. The typical Qui Tam Lawsuit under the False Claims act can take up to a decade of time in litigation.
Here is the DOJ “how to” guide:
https://www.justice.gov/civil/report-fraud
Report Financial Fraud to the Federal Government
If you believe that you have knowledge of financial fraud against the Federal Government – including fraud against other federally funded entities – there are several ways to report this fraud. The most commonly used methods are by reporting the fraud to the federal agency that has been defrauded, by notifying the Federal Bureau of Investigation (FBI), or by filing a “qui tam” action in federal court pursuant to the False Claims Act.
1. Notify the Federal agency harmed
All federal agencies have an Inspector General whose duties include investigating fraud committed against their agency. A directory of all federal agency inspectors general with their hotline number and address to report fraud can be found at the Council of Inspectors General on Integrity and Efficiency Directory webpage.
Troubled Asset Relief Program (TARP): If you are aware of fraud, waste, abuse, mismanagement, or misrepresentations affiliated with TARP, please contact the SIGTARP Hotline on the internet or by phone at (877) SIG-2009.
Health care fraud: To report health care fraud call 1-800-HHS-TIPS (1-800-447-8477) or submit a hotline complaint online.
2. Notify the FBI
You can report fraud to the FBI at the FBI’s tips and leads webpage. You also can contact your local FBI office. To find your local FBI office, visit the FBI’s Your Local FBI Office webpage.
3. File a qui tam action under the False Claims Act (FCA)
The FCA was first enacted in 1863 to fight fraud against the Federal Government. Under the FCA, individuals can file a complaint in federal court alleging financial fraud against the Federal Government. Because there are important procedural requirements involved in filing a False Claims Act qui tam action – such as filing the complaint under seal – many individuals obtain legal counsel before filing a qui tam action. Individuals who satisfy FCA rules regarding who may pursue qui tam actions, and whose lawsuits result in a recovery for the Federal Government, are entitled to a share of the government’s recovery.Updated June 24, 2019
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https://www.justice.gov/sites/default/files/civil/legacy/2011/04/22/C-FRAUDS_FCA_Primer.pdf