It appears there is no such thing as "instant" background check for ammunition.
...and having (re)read the California gun "eligibility" laws again, I once again resolve never to step foot in the state that I once called home during the 50's, 70's, and 90s -- and regarded as truly magnificent.
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The person is not prohibited from purchasing or possessing ammunition. The Department determines eligibility based on a comprehensive review of its records (similar to a firearm eligibility check).
Please note: this eligibility check requires a manual review of records by a Department analyst. As such, the Department may take longer to respond with a determination as to eligibility. Response times may take several days
https://oag.ca.gov/firearms/apap
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Freedom is a fragile thing and is never more than one generation away from extinction.It is not ours by inheritance; it must be fought for and defended constantly by each generation, for it comes only once to a people. Those who have known freedom and then lost it have never known it again.
January 5, 1967: Inaugural Address .... as Governor of
California