I want to play a game with my best friend. She used to live very near me and we could play minecraft on the same server the whole time. But now she has moved house and we hardly see each other, and we need to play on the same server, just without being on the same internet. How do I do this?
There are a few options that you have to do this. They do however vary in difficulty but they should all work.
First of all, you can either use an actual server hosting application eg. the Minecraft server application which comes in a .jar file format on the Minecraft website under somewhere in the download section. (once you have it you can look up how to use it online.)
you can still use the "open to lan" button, however, you will need to find a way to "forward" it to the world wide web aka the internet.
You could go the route of hamatchi (I haven't used this myself but a quick google search should tell you how to use it with Minecraft)
Another Option is Good old Port Forwarding
These are the best options that come to mind right now. Keep in mind that these can in some cases open up your network to threats if done improperly.
Best Of Luck.
This is a duplication of a question asked 2 days ago.
"How do I play Minecraft with friends without being connected to the same wifi network?"
Though it sounds like you were already playing on a public server. If that is true(and it is still online), she should still be able to log into that server.