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"a shared interest in" is correct and commonly used in written English.
It is usually used to describe a topic or activity that is of interest to multiple people. Example: "John and Sarah had a shared interest in hiking, so they often went on weekend trips together to explore different trails."
Exact(59)
Hooper and England's current head coach worked together at Leeds a decade ago and have a shared interest in team-building that still endures.
His friendship with Mr. Obama evolved into a shared interest in the problems of urban education.
A shared interest in the federal statistical system brought Granquist and Caddell together.
She said a shared interest in a toy could help foster that bond.
We have common goals, and a shared interest in achieving them.
The unlikely pair bonded over a shared interest in hi-fi.
He attributes a breakthrough in negotiations with a Saudi prince to a shared interest in farming.
Superficially, Norton and Chambers have a shared interest in ecclesiastical matters.
And second, of course, they have a shared interest in money.
But they soon became close, finding a shared interest in food and design.
It was a shared interest in politics that initially brought the members of WHW together.
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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