The phrase "after moving through" is correct and usable in written English.
It can be used to describe a sequence of actions or events that occur following a process of transition or passage.
Example: "After moving through the dense forest, we finally reached the clearing."
Alternatives: "after passing through" or "after traversing".
After moving through the racing circuits, he became a test driver for Kelley Racing in 2002.
He started his N.F.L. career with the Ravens in 1999, after moving through the college ranks.
After moving through Trujillanos, Deportivo Táchira and Mineros de Guayana, he took Deportivo Anzoátegui to second place in the Venezuelan league.
After moving through a broad spectrum of forms from social realism to ecological fable, she returned to scenes of crime later with books such as Blackwater.
On his home soil, after moving through the youth and under-21 ranks, Ronaldo had made his first appearance for Portugal's full national team against Kazakhstan in August 2003 (four days after his debut for United).
After moving through the baggage claim, they reach an abundance of kiosks belonging to Mashhad's various expensive and luxury hotels, where Iraqi passengers have a far warmer treatment than at Mehrabad.
As they lounged with Ron Marli in the Avac center office, the building rumbled with the vaguely digestive thrum of after-lunch waste moving through the pipes.
After combat forces moved through, the brigade and the Kuwatis then sealed off ten of these breaches to prevent Iraqi forces from using then, leaving two open for US forces that followed from the 82nd and 101st.
After decades moving through the revolving door between the private sector and government service, Gregory B. Craig has landed again at the White House, serving as counsel to a young administration in need of a steadying hand.
After easily moving through the preliminaries and semifinals, Soni struggled in the second half of the race, touching in 2 21.47 to hold off Yuliya Efimova, near left, of Russia (2 22.22) and Martha McCabe of Canada (2 24.81).
Sarah Hughes won a sure sweetheart's place in the heart of America when she rose from fourth in the skating short program to first after moving flawlessly through a challenging long program.
