Please check my sentence if it has error
The first sentence is not correct. e. she arrives a short time after him).
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The first sentence is not correct. Possibly you mean something like "He has not been there long when she arrives" (i.e. she arrives a short time after him). The second sentence is correct English in itself. The last sentence is ungrammatical, and I can't understand what it is supposed to mean.
It is relatively unusual (though not wrong, of course) to describe events in the present tense
I mean
It is just his time for using the equipment has not been over yet