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The phrase "after the formation" is correct and usable in written English.
It can be used to refer to a time period or events that occur following the establishment or creation of something.
Example: "The team will review the project outcomes after the formation of the new committee."
Alternatives: "following the establishment" or "subsequent to the formation".
Exact(58)
Soon after the formation of the board, which had only advisory powers, the strike ended.
After the formation of a transitional government in July 2011, the embassy reopened in September.
One member was taken in after the formation of the club, Frederic N. Watriss.
Many predicted a wave of consolidation after the formation of Diageo, but for various reasons no such trend emerged.
Tells about a visit to Kennedy's office on Oct. 31 2 days after the formation of the Kennedy for Pres.
"After the formation of the sun, the vast majority of mass left over in the solar system resides in Jupiter.
Inter-factional violence flared again in the Gaza Strip, days after the formation of a national unity government.
For ten years after the formation of Transport for London (TfL), the capital's bus service was a huge success.
"No clear leadership emerged after the formation of the state," said Professor Xavier.
He resigned in 1855 shortly after the formation of the 3rd Viscount Palmerston's first ministry.
American forces are at a higher state of alert this week after the formation of the first postwar government since Saddam Hussein was deposed in April.
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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