The phrase "acknowledged a link between" is correct and usable in written English.
You can use it when discussing a recognition or acceptance of a relationship or connection between two or more subjects.
Example: "The researchers acknowledged a link between diet and mental health in their latest study."
Alternatives: "recognized a connection between" or "identified a relationship between".
Recently, however, the United States has acknowledged a link between human activity and global warming.
An NFL official has acknowledged a link between football and a degenerative brain disease for the first time.
His lawyer, Edward Fitzgerald, acknowledged a link between the group and Mr. bin Laden, but said it was a peaceful group seeking reform in Saudi Arabia.
Goodell's comments on Wednesday at the annual owners meetings directly referenced NFL senior vice president Jeff Miller, whose remarks to a congressional roundtable last week represented the first time a league official has acknowledged a link between football and CTE by a league official.
In March, an NFL official acknowledged a link between football and CTE for the first time when Jeff Miller, the league's senior vice-president for health and safety, spoke about the connection at a roundtable discussion with the House committee on Energy and Commerce.
The agreement came after the jury had heard from some key witnesses, such as Boston University neurologist Robert Cantu, and also considered a deposition from the NCAA's chief medical officer, neurologist Brian Hainline, in which he acknowledged a link between football and degenerative brain disorders like chronic traumatic encephalopathy.
The £336,078 Big Lottery grant acknowledges a link between welfare reforms and mental health problems.
"It's an intrinsic component of football". The NFL acknowledges a link between football and CTE, or does it?
The Conservative-Liberal Democrat coalition persistently refused to acknowledge a link between its economic and social security policies and the explosion in food banks.
The keynote in nearly all of them is gratitude, for in the long perspective a writer must acknowledge a link between nurturing an offspring and nurturing a talent – both of them blood-deep, life-defining and mysterious.
The program doesn't give the league much credit for recent rule changes and other safety initiatives, instead underscoring its continuing reluctance to acknowledge a link between the sport and brain injuries and its reliance on language that pushes any day of reckoning into the future.
