In GBEng, assuming 'just' here means 'a moment or not very long ago', you'd write:
She's just left me!
Why? Because although the act took place in the past, the consequences are still felt in the present - so there's a past-present sense for which we would use the present perfect. You could think of it like this, where I give a possible consequence:
She's just left me [and I'm feeling completely lost now]!
Note, if you anchor this sentence in the past you would use the past simple:
She left me yesterday.
She walked out a moment ago.
Here you are simply talking about a past action and there is no indication of present consequences.
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