According to the BSA/AML Manual1, a financial institution is required to file a SAR for any transaction conducted or attempted by, at, or through the institution that involves or aggregates at least $5,000 in funds or other assets, and the institution knows, suspects, or has reason to suspect that the transaction (or a pattern of transactions of which the transaction is a part): (a) involves funds derived from illegal activity or is intended or conducted in order to hide or disguise funds or assets derived from illegal activity; (b) is designed to evade any requirements of the BSA or its implementing regulations; has no business or apparent lawful purpose or is not the sort in which the particular customer would normally be expected to engage, and the institution knows of no reasonable explanation for the transaction after examining the available facts, including the background and possible purpose of the transaction; or (d) involves use of the institution to facilitate criminal activity. In this case, Bank A is the institution that processes the wire transfer and deems it suspicious, based on its own assessment of the transaction and the customer. Therefore, Bank A is responsible for filing a SAR for the transaction in Country A, where it is located and where the transaction takes place. Bank A does not need to file a SAR for the transaction in Country B or Country C, as it does not have jurisdiction or authority over those countries or the other banks involved. However, Bank A may share information about the suspicious transaction with Bank B or Bank C, subject to certain conditions and limitations, as described in the BSA/AML Manual1.
References:
BSA/AML Manual1
Suspicious Activity Reporting - Overview2
Suspicious Activity Report (SAR) Basics3
From Microsoft Start Partners
Another simpler way of looking at the problem is by seeing this case as a Correspondent Banking relationship:
-A is the primary correspondent bank.
-B is the respondent bank.
-C is the receiving bank (of the wire transfer).
Since A is conducting the transaction on behalf of B's customer via the correspondent relationship deemed suspicious, it is the transaction in Country A by the correspondent bank that files the STR. Also, per the regular process, it is on the transaction, not the bank, that the STR is filed against.

Explanation
An internal auditor with the requisite knowledge and expertise of AML: An internal auditor with sufficient knowledge and expertise in AML regulations and compliance requirements can perform the AML audit.
Qualified bank staff if not involved in the AML function being tested: Qualified bank staff who are not involved in the AML function being audited can perform the AML audit.