That aside, even if Japan has agreed in certain areas to have the same law as the USA that definitely does not mean an order from an American court will be enforced in Japan. Even if the Japanese court is satisfied that the American court made the correct decision in law it still might decide that America was not the correct forum or that according to their laws the proper jurisdiction was Japan. In that case you'd have wasted tens of thousands and months/years of your time to get a court order that is worthless.
But not this part. Generally, as a matter of international comity, and pursuant to treaties to which both Japan and the United States are party, courts from one country do not act as appeals courts for those of another. So long as the proper procedure is followed, the United States and Japan will enforce a breach of contract judgment from a court in the other country.
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Would a freezing order would be enforceable? It is not a final and conclusive order.