Is it correct use of Present Perfect and Present Perfect Continuous with "after" in the sentences " After he started working, he has not taken a break yet", " After she learned the truth, she has thought it through very carefully", " After he got the job, he has been working hard for 4 months already"?

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In the first one I’d say since, not after. Since he started working, he has not taken a break yet.

In the second one I’d say after she learned the truth, she thought it through, or she has been thinking it through.