Okla. Stat. tit. 12, § 12-718.8
Stay of proceedings pending appeal of foreign-country
judgment.
If a party establishes that an appeal from a foreign-country
judgment is pending or will be taken, the court may stay any
proceedings with regard to the foreign-country judgment until the
appeal is concluded, the time for appeal expires, or the appellant
has had sufficient time to prosecute the appeal and has failed to do
so.