Short answer. Yes. Article 1269 of the Civil Code gives you, as creditor, all the rights of action the debtor would have had against the third person who caused the loss, once the obligation has been extinguished by that loss. You essentially step into the debtor's shoes to pursue the person responsible.
What the law says
The obligation having been extinguished by the loss of the thing, the creditor shall have all the rights of action which the debtor may have against third persons by reason of the loss.
Civil Code, Article 1269 — Creditor's Right to Actions Against Third Persons. Read the full provision →
Why you get a claim even though your debtor is released
When the specific thing owed to you is lost without your debtor's fault, the obligation to deliver it is generally extinguished, meaning your debtor is released from having to hand it over. Article 1269 addresses what happens next when a third person's fault actually caused that loss: rather than leaving you with nothing because your debtor is off the hook, the article transfers to you all the rights of action which the debtor may have against third persons by reason of the loss.
What stepping into the debtor's shoes means here
Because the rights that pass to you are specifically the debtor's own rights of action against the third person, the scope of what you can pursue is defined by what the debtor could have claimed had the debtor remained the one pursuing the loss directly. You are not given a freestanding claim independent of the debtor's position; you are given the debtor's own claim, transferred to you by force of this article because it is you, not the released debtor, who actually suffered the ultimate loss of the thing owed.
Why this transfer makes sense
This rule prevents an unfair result where the person actually responsible for destroying the thing faces no consequence, simply because the debtor who happened to be holding it was excused from delivering it to you. Since your debtor no longer has a personal stake in pursuing the third person, having already been released from the underlying obligation, Article 1269 makes sure that lack of interest on the debtor's part does not leave the actual wrongdoer beyond reach, by putting that claim in your hands instead.
What this means for pursuing the third person
Because you are exercising the debtor's own rights of action, establishing your claim against the third person generally involves the same kind of proof the debtor would have needed: that the third person's fault caused the loss, and what that loss is worth. Article 1269 supplies the legal basis for you to bring that claim in your own right, but the substance of what you have to prove about the third person's responsibility for the destruction remains tied to the facts of how the loss actually occurred.