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The phrase "After having completed" is correct and usable in written English
It can be used to indicate that an action has been finished before another action takes place. Example: "After having completed the project, she submitted her final report to the manager."
Exact(60)
After having completed the construction of it, the dynamometer was tested by performing drilling and measuring the forces, thrust and torque, on SAE 1020 steel.
After having completed substantial course work in the area of concentration, students must seek approval from the council faculty adviser for the research project they propose as the qualifying paper.
After having completed my freshman year, however, I realized that you learn just as much outside the classroom as you do inside it.
After having completed countless projects of varying sizes in Greece, Oikosteges is now ready to export its know-how to other countries with similar climates.
After having completed filming for The Last Song (2010) in Tybee Island, Georgia, Cyrus returned to Los Angeles, California for tour rehearsals at The Forum in mid-August.
After having completed the song, Hall complimented Carey's work ethic and form of writing, calling her a "perfectionist" and "very professional".
After having completed the 24-reel cut of Greed, von Stroheim told Goldwyn executives that he could not cut another frame.
After having completed the baseline questionnaire, patients were assigned to either the intervention or control group.
After having completed at least 12 of the courses the farmers were given a diploma as an FFS farmer.
After having completed all four VAS's per screen, participants clicked a 'continue' button for the next screen.
After having completed 36 hours of hospitalization in the PICU with multiple cardiac arrests, the child was no more responding to resuscitation efforts and died.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com