The audit function should report to the audit committee of the board of directors (or similar oversight body) and independently evaluate the risk management and controls of the bank through periodic assessments, including the adequacy of the bank's controls to mitigate the identified risks, the effectiveness of the bank's staff's execution of the controls, the effectiveness of the compliance oversight and quality controls and the effectiveness of the training.

According to the BSA/AML Manual1, once a financial institution files a SAR, it should maintain a copy of the SAR and the original or business record equivalent of any supporting documentation for a period of five years from the date of filing the SAR. The supporting documentation should be identified and maintained by the financial institution as such, and be deemed to have been filed with the SAR. The financial institution should make all supporting documentation available to FinCEN or any federal, state, or local law enforcement agency, or any federal regulatory authority that examines the financial institution for compliance with the BSA, upon request. Therefore, the best action to take regarding a particular account once suspicious activity is reported by the institution is to secure all supporting documentation, as it may be needed for further investigation or examination.
References:
BSA/AML Manual1
Suspicious Activity Reporting - Overview2
Suspicious Activity Report (SAR) Basics3

Bank A should file a suspicious transaction report (STR) on the transaction in Country A, as it is the financial institution that observes and processes the suspicious activity in its jurisdiction. According to the FATF Recommendations, financial institutions should report any transaction that they have reason to suspect is related to money laundering, terrorist financing, or other criminal activities, regardless of the amount involved1. The STR should include information about the originator, the beneficiary, and the purpose of the transaction, as well as the reasons for suspicion2. Bank A should also comply with any legal or regulatory requirements in Country A regarding the reporting of cross-border wire transfers3.
References:
1: FATF Recommendation 20 - Reporting of suspicious transactions
2: FATF Interpretive Note to Recommendation 20
3: FATF Recommendation 16 - Wire transfers
Reference:
http://www.fatf-gafi.org/media/fatf/documents/recommendations/pdfs/FATF%20Recommendations%20(approve (page 19, DNFBPs: customer due diligence, bulleted point (b))

one of the key roles of FATF-Style Regional Bodies (FSRBs) is to support the system of mutual evaluation, which is a peer review process that assesses the level of compliance and effectiveness of each member country's anti-money laundering and counter-terrorism financing (AML/CFT) regime12. FSRBs conduct mutual evaluations in accordance with the FATF's methodology and standards, and share the results and recommendations with the FATF and other FSRBs3. Mutual evaluations help identify the strengths and weaknesses of each country's AML/CFT system, and provide a basis for technical assistance and follow-up actions4.
References:
What are the 9 FATF-Style Regional Bodies (FSRBs)? - Sygna1
FATF-Style Regional Bodies (FSRBs) - Asia/Pacific Group on Money Laundering2 The Role of FATF Style Regional Bodies (FSRBs) in Combating ... - IDMerit3
9 FATF-Style Regional Bodies (FSRBs) - fineksus.com4