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The phrase "aware of this fact" is correct and usable in written English.
It can be used when indicating that someone has knowledge or understanding of a particular piece of information.
Example: "I hope you are aware of this fact before making your decision."
Alternatives: "conscious of this fact" or "informed about this fact".
Exact(60)
Trump is well aware of this fact.
Unfortunately, nobody has made either party aware of this fact.
Paleo practitioners are well aware of this fact.
The Comment editor was not aware of this fact.
You're kind of a big deal round here - are they aware of this fact?
Ducati owners seem aware of this fact -- up to a point.
If Daniella Weiss was aware of this fact, she chose not to mention it.
They appear to be keenly aware of this fact, and so they wink at the audience.
Bragg was not aware of this fact, but Polk made no attempt to explain the reason for his insubordination.
The Stanford students who I talked with at the dinner were aware of this fact and were also constantly reminded of it by the speakers.
Researchers have found that while most of us are generally aware of this fact, few of us are adept at detecting actual lies in negotiation.
More suggestions(15)
informed of this fact
mindful of this fact
cognizant of this fact
aware of this funding
aware of this theatricality
aware of this hostage
aware of this kind
aware of this risk
aware of this point
aware of this distinction
aware of this problem
aware of this policy
aware of this difference
aware of this objection
aware of this split
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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