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The URL to query for each assertion is passed in an individual header or variable named Shib-Assertion-NN, where NN is the two-digit sequence number of the assertion(01, 02, etc). Performing a GET on that location will result in the assertion, with a MIME type of "application/samlassertion+xml".
Note that in order for export to occur, the exportLocation and exportACL properties must be set for the relevant application.