The phrase "been internalized" is correct and usable in written English.
You can use it to refer to something that has been adapted and accepted as part of someone's beliefs or behavior. For example, "The importance of following a healthy diet has been internalized by many people."
Dictionary
been internalized
verb
To make something internal; to incorporate it in oneself.
Exact(60)
Despite this, these results clearly indicate that this method can be accurately used not only to assess whether a bead has been internalized or not, but also to establish a rate of internalization by counting the number of beads that have been internalized at a given time (further details on the kinetics provided later in the Results).
What was once shocking and unacceptable in America has now been internalized as the new normal.
Here's its been internalized that this is the way we deal with any issue.
"Frustration and anger have been internalized on the part of the Palestinians as well as the Israelis.
"It has been internalized now as part of our national iconography, and it has become our symbol of ourselves".
"The realities of the minority majority have not yet been internalized," according to Bruce Gyory, a veteran political consultant.
The values propagated during General Zia's long rule and entrenched in the law have been internalized by some sectors of society.
In the late seventies, the automatic gesture of obeisance to feminism had not yet been internalized by academics, and an amused hostility was still the norm.
While the commercialization of the book business has been internalized by those who toil in it, industry experts say that commercialization is not incompatible with quality.
The secular idea, the state system and the balance of power, pop culture jumping tariff walls and barriers, the state as an instrument of welfare, all these have been internalized in the remotest places.
It is in D minor, the iconic tragic key of Mozart and Beethoven, although the steady pace suggests that tragedy has been internalized, made into a way of life.
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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