BATF only takes stolen/lost firearms info from an FFL who is reporting the theft/loss from their inventory (shop or a shipment.
The FFL must first get a L/E agency to actually take a Stolen/Lost firearm report.
With that, the CR# from that report is needed when contacting the BATF to make that report to them.
IIRC the FFL has something like 24 or 48 hrs to report a gun missing from their inventory.

What the BATF does with the info is really irrelevent.

With a crime-stolen firearm/or lost firearm report taken by any L/E agency in the USA,,the firearms info will be entered into NCIC in the GunENT system anyway.
Any agency anywhere running that ser# will get a hit on the firearm with the corresponding misc descriptive info of the firearm and the reporting agencys info for contact.
NCIC searches and hits on the ser# only. So sometimes multiple hits come back and the operator has to sort out the info with the descriptive info.

The biggest problem is getting any L/E agency to actually take the report when this type of situation is involved,,,long distance shipping, interstate.
That gets kicked down the road generally.
The usual questions..
How do you know it was actually stolen ?
Where was it actually stolen from?
Where was it last and who had it.?

L/E agencys don't like to have stolen firearms reports in their yearly #'s.

I went through that twice as an FFL.

Hope your rifle gets back to you.
Shipping firearms is a headache and getting worse every day.