I would at the very least file a police report. A SAR is a different story - do you know who did this, if so, maybe under the identity theft reason - that sounds like what the person was after.
More importantly - don't worry about the "current loss", did the customer give out the info and if so, what have you done to help the customer prevent further theft "future loss" - recommend that they notify the credit bureaus, changed their accounts or put watch flags on them.....
_________________________
The opinions are mine and do not necessarily reflect those of my employer.