I may be misreading and need to check more carefully, but under Article 31 of the Montreal Convention , it would seem that you have 21 days to lodge the claim
Originally Posted by Montreal Convention
Article 31 — Timely Notice of Complaints
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2. In the case of damage, the person entitled to delivery
must complain to the carrier forthwith after the discovery of
the damage, and, at the latest, within seven days from the
date of receipt in the case of checked baggage and fourteen
days from the date of receipt in the case of cargo. In the
case of delay, the complaint must be made at the latest
within twenty-one days from the date on which the baggage
or cargo have been placed at his or her disposal.
In this case I would be getting back to AA and claiming for the loss of the bag - the limit of liability is 1131 Special Drawing Rights (USD 1,588.37 )