Contact numbers for the IRS should be in the blue pages of your phone book. However, it is unlikely you will be able to locate anyone willing/able to have a verbal discussion about what the problem might be with a customer's SSN. Here's a
thread about the verification services that are available.
If the customer is willing to cooperate and the number is an SSN, he or she needs to go to the SSA and request a form SSA-7028. If the number is an EIN, the customer needs to go to the IRS and obtain a form 147C. Both forms are referenced in the B Notice. They validate the number and, if you receive a copy, you can forward it to FinCEN.
If the customer is not willing to cooperate further, you should write back to FinCEN and describe your efforts to verify the name/TIN combination and ask for instructions. (You don't mention what verification the customer has offered, but add to that any information reporting you have done on the same name/TIN combination.) It's doubtful that you will get a response.
There are some problems you cannot fix and you can't invest too much more time on this one.