The Belgian bank should freeze the assets of the customer and report to OFAC, as this is the required action for any US person or entity, or any person or entity within the US, that holds or controls property or interests in property of a person or entity on the OFAC Specially Designated Nationals and Blocked Persons List (SDN List). The SDN List is a list of individuals and entities that are subject to US sanctions and whose assets are blocked by OFAC. The Belgian bank, by maintaining a branch in New York, is subject to the jurisdiction and authority of OFAC, and must comply with its regulations and directives. Allowing transactions, closing the account, or continuing business as usual would violate the sanctions and expose the bank to civil and criminal penalties.