“She's already moved on.”
You're gossiping about a friend of yours who's recently separated from his wife. You think that he's still hung up on her, but she's started dating other people and doesn't seem to care about him. This is how you describe the situation.
She's already moved on.
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(someone) has already (done something)
The word "already" is most commonly followed by a perfect verb like "done":
I've already given him something.
Have you already chosen where you're going on your honeymoon?
You can also use "already" with a simple past tense verb like "did":
I already gave him some food.
But this is more casual and less common.
To "move on" from an experience means to stop thinking about it, and start doing other things instead. Some examples:
Clementine's husband passed away two years ago and she still hasn't really moved on.
OK, if everyone's clear on that, let's move on to the next topic.
You use the words "from" and "to" with "move on". You "move on from" the experience that you had before, and "move on to" the next experience:
Some people never really move on from their high school glory days.
I've been working there for over five years, you know? I'm ready to move on to bigger and better things.