Using the same player when I connect to a local phone server from a different device?

Well, after some time, I figured out how to do it - pretty simple, may I say. So, if you have more than one device that you want to use as clients that connect using the same identity, you need to change the Minecraft PE client ID on the devices you want. This client ID is contained within the clientId.txt file.

Let the "server" alone, you don't need to mess with it for this.

Under Android, clientId.txt is in the /sdcard/games/com.mojang/minecraftpe folder. You just need to open the file on the 2nd device, replace the ID inside by the ID you found on the same file from the 1st device and you're ready to go. Any server, from now on, will recognize both devices as the same player. You can play on a device, leave the world, connect again with the other device and you'll be at the same point (with same items, XP, etc.) where you last left.

It's important to know that you CAN have different names, if you wish. It's the client ID that matters.