I have a different take from "doc" on the "only after..." part.

The last carrier is responsible for delivering your baggage to you, and for any compensation claims. If there is mishandling on carrier A's part, carrier B can go against them for that. You should not be responsible for chasing down carrier A.

Carrier B may choose to blame, point fingers, etc. etc. but the fact remains that they are the carrier responsible for delivery. Any compensation claims should be made against the delayed baggage report filed with carrier B at the arrival airport.

Even if your baggage fails to appear at an intermediate point (for instance Customs at the first port of entry, before connecting to a domestic sector), you do not (ordinarily) file a missing baggage claim until the end of the journey. You should, however, complete an authorization to permit the carrier to clear your bags for you, and interline them to the next carrier.