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The phrase "a week following" is correct and usable in written English.
It can be used to indicate a time period that occurs one week after a specific event or date.
Example: "The meeting will take place a week following the conference."
Alternatives: "one week after" or "a week later".
Exact(60)
Amici briefs are due a week following submission of the parties' briefs.
Typically, a person is contagious for at least a week following onset of symptoms.
Most formulations persist on foliage less than a week following application.
We are continuing to solicit comments for a week following the meeting, through Saturday, November 21 (midnight EST).
The national meteorological agency warned that aftershocks could strike for up to a week following the main event.
In little more than a week following the election on 6 May, €3bn was withdrawn from bank accounts.
As the press release states: "Within a week following the treatment, the patients experienced a variety of complications, including vision loss, detached retinas and hemorrhage.
Justin Lemieux, a Stanford emergency medicine physician, deployed as the team doctor for FEMA Task Force 3 about a week following the outbreak of the fire.
A week following injury, continuous micro-pump infusion of A13 (0.5μg/g/dand and saline was initiated for 4-week duration.
The proposed timetable for the company's £1.6bn takeover by Deutsche Bahn has slipped by a week, following discussions with the European Commission.
Among other things, she managed a cat hotel, then spent a week following an MEP, and found that working in advertising was unexpectedly exhilarating.
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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