Exclusive: Celebrity Hackers are Not Just After Publicity

The hackers who obtained Michelle Obama's financial records -- along withsome of the biggest celebs in the world -- aren't just seeking recognition ... law enforcement sources tell TMZ they have been "using" the credit information.

Our sources would not be specific on how the information has been used, but it could involve access and withdrawal of money.  As we previously reported, the hackers have obtained personal banking information as well as social security numbers and that could be enough to obtain withdrawals of cash.

We're also told the FBI has been "aggressively investigating" the case ... and it also strikes close to home, because one of the victims is FBI Director Robert Mueller. 

Our sources also make it clear ... the FBI knew about the hackers before they made themselves public.  We're told, "The investigation did NOT start yesterday."