Multiple repeat questions on the same issue. No. Cannot. Again, talk to your school's DSO about this. Once you file FOIA will most likely obtain a copy of the missing Notice of Action. That's what you'll need to use. Not the FOIA filing receipt!
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Although as the requestor, you can file a FOIA request, this may not be the best mechanism to achieve your goal. For example, a "lost" I-797A that never made it to the USCIS will not be available through FOIA because, as you stated, it was lost.