"found the encounter" is correct and usable in written English.
You can use it when you experienced or observed something unexpected. For example: I found the encounter between the two warring nations to be unexpectedly peaceful.
I found the encounter disturbing.
Mr. Booker found the encounter troubling.
She found the encounter thrilling, and convinced Mark that she should return, alone.
The British found the encounter "somewhat unsatisfactory", as the ambassador, Viktor Popov, appeared unmoved.
She found the encounter frightening, she told me some years later, and as soon as she came home, she told her partner they would be leaving Moscow.
Q: The godmother of your daughter, Shirley MacLaine, writes in her new book that you sighted a U.F.O. over her home in Washington state, that you found the encounter extremely moving, that it was a "triangular craft, silent and hovering," that you "felt a connection to your heart and heard directions in your mind".
But from the brain's point of view, a recent study has found, the encounters have much in common.
I have sat in countless coffee bars with people I'd thought a few weeks previously were my best buddy, and more often than not have found the encounters depressingly sticky once we have gone through the "What's so-and-so doing now?" phase.
Weinstein appeared to find the encounter unremarkable.
"There will be many victims of IRA terrorism who will find the encounter difficult, but the peace process is about tackling the difficult issues and making the difficult decisions".
Some employees find the encounters with the poor so searing that they do go back.
