Forgetting someone, means you try to move on as if they weren't in your life. Not happening with the majority of people.
Moving on and not forgetting is difficult, but technically moving on in any way would be difficult. Don't cling, if she wants to communicate, then go ahead. If you want to communicate then go ahead. Move on, without shutting out that person, do what you want. You are surrounded by thousands and millions of people. Online you have access to people all over the world. Family and other friends are always there , for many anyway(let's not get into this)
Basically, you can move on, and still be able to try and form a new friendship with an old friend. There's no point in forcing something that may not happen, but it doesn't hurt to try something if the chance comes up.
I'm not you, so idk you or the other person well enough to give advice, but this is the best I got with the information given. Everyone's problems are unique to some extent, no one understands what's happening better than you do. You can take the advice of the others that have been in similar situations, and try to come to your own understanding. It's difficult, but once you try and move past all the problems, and come up with the most 'convenient' (I mean as in, not being jerked around, like you're on a leash)
way to move on and be happy, you'll simply be happy
Edit: Today I stumbled upon something that kind of explains what I was trying to express.http://www.funnyjunk.com/channel/feels/ ... t/nvfsGai/