"deeply imprinted" is correct and usable in written English.
You can use it to describe something that has been very strongly, permanently, and sometimes emotionally imprinted on someone's memory. For example: "The image of his mother's face has been deeply imprinted in his memory."
Stallone's version is too deeply imprinted on our collective imagination.
Respect for birth-order privilege seems deeply imprinted.
Though the land is deserted, the signature of human habitation is deeply imprinted upon it.
If Eagleman's body bears no marks of his childhood accident, his mind has been deeply imprinted by it.
The Opus 18 quartets (1801), particularly No. 1, have Haydn's stamp deeply imprinted on them in their geniality, innovation and wit.
The bottom line is that leaders need to understand and harness the tribal psychology that is deeply imprinted onto the human brain.
"They make you realize how spatially based so many memories are and how deeply we're imprinted by our childhood homes".
The images of the towers crashing down, and the emotions around that event, is imprinted deeply.
Imprinted deeply into my memory of that day was the enthusiasm of Jordana as she eagerly turned the book's pages, the shy laughter of her brother who followed along, the children's sophisticated dialogue as they discussed the story and the brimming pride of Koffsky as she soaked in the cadence of Marcie Greenfield Simons' reading about Noah.
But the sensations--wrenching, exhilarating, deeply imprinted--are readily rekindled.
In the decade or so since the group broke up (not counting a brief comeback in 2006), Mr. Dulli has taken on plenty of secondary gigs (the Twilight Singers, the Gutter Twins), but none have imprinted as deeply as this band, which was an arena-sounding cult act about two decades before that became widely acceptable.
