I was visiting the US (I live in Central America)and we were at a public mountain look out for the sunset and on our way back to the car?

We found an iPhone on a railing. It was cracked up pretty badly, the whole screen was shattered, chipped on the sides and you could seen the internals of it by the home button and the six port was smashed inward. We called out if anyone lost there phone. Nobody acknowledged and it was getting dark, and by the condition of the phone, I looked like it had been run over or dropped off the cliff we were on. Plus the phone wasn't turning on so we didn't know if it was dead or out of battery. But it turned out it was just out of battery. We took it back to our rental house and waited for someone to call. We had it for 4 days and nobody called but robot credit card information calls. We left the country and I forgot that it was in my bag. Now the phone doesn't have cell service and I don't know what to do. I feel bad and still want to get it back to him but I don't know how to start. What should I do? The only notifications on the screen were some dating apps and from that I got his name. There was also one Facebook notification that said ___ liked your photo. So we looked up that persons name and found someone who had that name and lived in the area and asked if her friend had lost his phone on the mountain we were on. She never replied. And since we had to charge the phone we could access Siri. I feel bad and still want to get it back to him but I don't know how to start. What should I do?

This is the phone

It was probably lost. Then somebody found it and put it on the railing (assuming the person who lost it would come back). It could have been there for a long time and the person probably moved on and reported it lost. I wouldn't worry about it too much.

You've done all you can, pity you didn't leave it in the US.