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The phrase "after they reached" is correct and usable in written English.
It can be used to indicate an action that occurs following the completion of reaching a destination or goal.
Example: "After they reached the summit, they took a moment to enjoy the breathtaking view."
Alternatives: "once they arrived" or "after they got to".
Exact(60)
He shook hands with Cox after they reached the plate.
Three patients had their UBA performed after they reached ESRD, in preparation for renal transplantation.
After they reached their destination, most of the mules became diseased and had to be shot.
It insured the children of military personnel at preferred rates even after they reached adulthood.
After they reached eight successive correct responses to each image, the non-rivalrous condition was terminated.
The touring side's lead has swelled to 261 after they reached 172 for three at stumps.
In 1985, he ordered the city to provide help to foster children after they reached 18.
But they aborted the plan when Ms. Belnavis started hyperventilating after they reached the second floor.
He sold his holdings in Arch and Massey last year after they reached his price targets.
In 1847 alone – "Black 47" – 50,000 perished en route to the new world, or shortly after they reached it.
Officials said Tuesday that a deal was imminent, after they reached agreement in principal on reopening the transit corridors.
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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