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The Event Frame searches are actually stored in the HKCU registry. So if you want everyone to have the same search, you would need to export your HKCU key and push it to the user through GPO (or manual export / import).
Disclaimer: Do not use a registry editor to edit the registry directly unless you have no alternative. The registry editors bypass the standard safeguards provided by administrative tools. These safeguards prevent you from entering conflicting settings or settings that are likely to degrade performance or damage your system. Editing the registry directly can have serious, unexpected consequences