If you still are able to access the files on your Galaxy J3 prime, you can go to the following directory using any file explorer:
/sdcard0/games/com.mojang/minecraftWorlds/... (you do not require to have a rooted phone for this)
from there you can copy the world and send it to your new phone (send via email, bluetooth, file-sharing websites, etc.), and then copy the world file to your new phone in the same directory.
You mentioned using only your new Galaxy A20 to transfer the world file to your new phone. This is not possible unless you have a cloud backup of the world, since you would still need to have file access to your old phone to get the world.