system
Given the following post, respond as if you're commenting on Reddit:
human
[Coco] How did Miguel prove Hector was the true artist of La Cruz's work?

Think about it. What if some kid showed up tomorrow claiming that their great-grandparent was the true writer of Elvis Presley's music? Elvis is no longer around to confirm or deny these allegations and the kid has no evidence to show for it other than their word. Would we all just roll with that claim? What proof did Miguel have to support this? Coco kept letters and poems from him, they could just crossreference his handwriting to the songbook right? Sure, but did they have the songbook? Yeah he had the photo of Hector with the guitar, but if him and Ernesto had matching uniforms why couldn't they have matching guitars? Hell, even Miguel had a matching guitar that his abuela smashed. "They got de la Cruz to confess!" Yeah, in the Land of the Dead. The Living never heard any of that. Miguel would have to do quite a bit of digging to make a strong enough case to transfer all credibility back to Hector. Also, even if he did find enough handwriting evidence to make his case, how would he prove the murder bit?
gpt
Postage marks.

There's an idea called "Poor Man's Copyright" where you can prove the date something was written by simply mailing it to yourself, since the Post Office will stamp the envelope with the date.  Now, this wouldn't actually give the family copyright, but it would be enough to prove that Hector wrote the lyrics first.

Hector wrote the lyrics for most of de laCruz's best songs as poems for his young daughter, which he included in the letters he sent home.  She saved the letters and, crucially, the envelopes they arrived in.  Each envelope has a date on it corresponding to the date that Hector mailed it to her.  Those dates prove that Hector Rivera and not Ernesto de laCruz originally wrote those songs.

Whether Ernesto saved the original songbook or not, and even if he did it's unlikely his estate would want to give it up for an analysis of the handwriting, the letters would be enough to prove that Hector was the real lyrical genius.

Similarly, photographs from the time would show that laCruz's distinctive guitar originally belonged to Hector Rivera.  There could also be photos of both musicians in local newspapers, as they were touring at the time.  Hector owned the guitar first, Ernesto came into possession around the time that his partner died.  Seeing as he clearly stole the lyrics, it seems he also stole the guitar.

Proving murder would be harder, but given that Hector's last letter would also indicate that he was giving up on touring and returning home, as well as the town he was in, it might be possible to find mortuary records from that town.  If the records went back far enough, the Riveras could find proof that a musician matching Hector's description died of "food poisoning" right around the same time.  Not proof, but very suspicious along with the above.