Short answer. Yes. The Civil Code allows this: once you discover a deposited thing was stolen and advise the true owner of the deposit, if the owner still does not claim it within one month, you are relieved of all responsibility by returning the thing to the depositor.
What the law says
If the owner, in spite of such information, does not claim it within the period of one month, the depositary shall be relieved of all responsibility by returning the thing deposited to the depositor
Civil Code, Article 1984 — No Duty to Prove Ownership; Stolen Things. Read the full provision →
What the law says
should he discover that the thing has been stolen and who its true owner is, he must advise the latter of the deposit
Civil Code, Article 1984 — No Duty to Prove Ownership; Stolen Things. Read the full provision →
Why you were not free to ignore the discovery
A depositary is not normally required to investigate or prove the depositor's ownership before accepting a deposit; the general rule is that the depositary cannot demand that the depositor prove ownership. But once you actually discover that the thing has been stolen and who its true owner is, the law imposes a specific duty: you must advise the latter of the deposit. You already did this, which is exactly the step the law requires once the discovery is made. Notifying the true owner is what protects you going forward, rather than simply sitting on the information.
What the one-month silence means for you
Having advised the true owner, the law then gives that owner a one-month window to come forward and claim the item. If the owner, in spite of such information, does not claim it within that period, you as the depositary are relieved of all responsibility by returning the thing deposited to the depositor, meaning the person who originally left it with you. The month has already passed in your situation, and the true owner did not act on the notice you gave, so the condition for safely returning the item to the depositor has been satisfied. It is worth keeping some record that the notice was actually given and when the month lapsed, since being relieved of all responsibility rests on those two facts being true.
One situation where returning it would not be safe
The same provision also gives you a separate, independent option: if you have reasonable grounds to believe that the thing has not been lawfully acquired by the depositor, you may return the same, meaning return it to the true owner instead, rather than to the depositor. If you have genuine reason to doubt the depositor's own claim to the item beyond the fact that it was stolen from someone else, that doubt is a separate basis for withholding the item from the depositor even after the one-month period has run.