I've looked. And looked... And looked.
And it doesn't look like Minecraft actually supports this.
There are two possible ways you could do this:
The easy way) You get your friend to host the realm. I mean, you're both using it and it's not expensive.
The hard way) Get your friend to get Minecraft Realms trial. Have him upload the world. Get him to log in to a PC copy of bedrock and download a copy of the realm. It may take some jiggery pokery, but you should be able to use that local copy of the map using your account on the same PC. Now you have your own copy of the map, you can get your Realms account and upload it to your realm.
To be honest, I'd go with the former. I have a realm for me and my nephew and it costs me about £3 a month. Not the kind of money that people often end up fighting over.