We are having a debate on SAR filings. If we have a customer that we have filed continuous activity SARs for and no the activity is stopped after an account is closed or we have determined that the reason for the activity is not suspicious do we need to file a "FINAL" SAR explaining that this is the last SAR or do we just stop filing SARs and document our internal files on why another continuous activity SAR was no filed?

There is no such thing as a "FINAL" SAR. If the suspicious activity has stopped, you should document such during your review of the relationship and move on.

"the activity is stopped after an account is closed"

Well I surely hope so