Our arbitration is under the additional facility rules, which have no mechanism of appeal or annulment as in the standard rules.

Once an award is obtained under the AFRs, you file for enforcement under the rules of a court in a country where the respondent has assets. For example, in the US you would file in a federal district court. The action is governed by 9 U.S.C. § 207, which states:

"The court shall confirm the award unless it finds one of the grounds for refusal or deferral of recognition or enforcement of the award specified in the said Convention."

The Convention referred to is the 1958 New York Convention that set up the international arbitration process. The word "shall" means that the judge has no latitude unless a specific ground is present and none of those are possible in our case.

Moreover, 28 U.S.C. § 1605 specifically waives sovereign immunity in the enforcement of arbitration awards "governed by a treaty or other international agreement in force for the United States calling for the recognition and enforcement of arbitral awards."

Here is a good quote that sums up the matter:

"Where these requirements are met, international arbitration
awards are readily confirmed. United States courts liberally favor
recognizing and enforcing foreign arbitral awards. In order to
enforce an international award, the party seeking enforcement
must simply provide to the court a certified copy of the award and a
certified copy of the arbitration agreement. One effect of the
widespread acceptance of the New York Convention is that “[i]t is
far easier to enforce an arbitration award worldwide than it is to
attempt to enforce a civil judgment."

http://usadr.com/sites/default/files/enforcing-arbitration-awards.pdf at 1310.