The phrase "a final encounter with" is correct and usable in written English.
It can be used when referring to a concluding meeting or interaction with someone or something, often in a narrative or reflective context.
Example: "As the story unfolded, the protagonist prepared for a final encounter with the antagonist that would determine their fate."
Alternatives: "a last meeting with" or "a concluding confrontation with".
Xerxes returned home, but the Persian general Mardonius remained for a final encounter with the Greeks at Plataea.
Is Miles killed by a final encounter with Quint, as the stage action suggests, or has the Governess either killed him or terrified him to death herself?
Instead, he found himself roped to a chair for a final encounter with Sansa, who coolly vowed to wipe out every trace of his legacy.
It is about a criminally insane schoolgirl and three hapless Hong Kong schoolboys who become tangled in a web of terrorism, bombings, animal abuse and a final encounter with gun-wielding Western bad guys.
The tale winds to a close with a final encounter between this honey-smooth villain and the woman he has tortured in the hopes of winning her over to the dark side.
In a final encounter in 2008, Bush joked with Robinson about still not wearing his hat.
Steven Moffat Amymy & Rory will leave in a final encounter w/ the Weeping Angels in ep 5.
But readers willing to settle for professionally wrought diversions should find pleasure in Stanley Ellin's Poe-like tale of vengeance, Evan Hunter's sharp look at a first offender's final encounter with the police and Robert L. Fish's droll puzzler about a wager with a twist.
But it was his second and final encounter with an animal the one that took place with Dolly at Floridaland that ended up making Brenner the unofficial spokesperson for the people who think animals can consent to sex.
But in the final encounter, with Habana a spectator, Williams scored twice as the Lions won 28-9.
Throughout, the dominant figure is her idol, Atherton, who she writes is "haunting my dreams"; her final encounter with him proves a beautifully observed exercise in subverting expectations.
