"the unforgettable" is a grammatically correct phrase and can be used in written English.
It can be used as an adjective to describe something that is impossible to forget or that leaves a lasting impression. For example: - The unforgettable sunset over the ocean took our breath away. - The unforgettable smell of freshly baked bread filled the air. - The unforgettable experience of swimming with dolphins will stay with me forever. - The unforgettable melody of the song brought tears to my eyes. - The unforgettable moment when we said "I do" will always be in our hearts.
Dictionary
the unforgettable
adjective
Which is very difficult to forget
Exact(54)
I was mesmerized by the unforgettable images.
It was the unforgettable lesson of freedom.
"The unforgettable is forgotten," Mr Pownall said.
There's the unforgettable music by David Raksin.
This'll be Marcus's summer, the unforgettable Summer of '09.
It got the unforgettable, climactic conclusion it deserved.
First Class William Solorzano described the unforgettable sound.
And of the cricket, of the unforgettable innings there is almost nothing.
The unforgettable intensity of their performance made it seem perfectly possible.
RIDGEFIELD Ridgefield Theater Barn "The Unforgettable Whatshisname," comedy by Myles Gansfried.
Then there was the unforgettable Game Six that will forever be part of baseball folklore.
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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