What is the most appropriate way to address someone being given a false PT score, while minimizing the damage to their career?

Non Commissioned Officer with integrity issues is useless. Gave up authority to lead.

Unless you actually witnessed the previous NCO giving a false score, you have nothing to say! If you are scoring her now, then you should offer to work with her to bring up her PT score. End of story.

I would think it would be dangerous to have an NCO who cannot be in as good physical condition as the troops he or she might command. If the soldier in question is really competent in other areas, I would offer to work with them, after hours, in order to get them in condition. In short, the soldier has to able to pass the test. The initiative has to be his or hers.

She should have spoken up as soon as she found out she got a false PT score.

Don't worry about her career. She has zero integrity and shouldn't be promoted in the first place.

AR 635-200, Chapter 13.
No integrity, get'm out.

In my book whether this soldier knew it or not, THERE IS NO EXCUSE; sounds like the rich parents who paid someone to get their kids into elite colleges and claim their kids were unaware of the fraud committed by their parents, that's total B.S. they must of have know, they knew they weren't that bright or participated on any of the sports mentioned to get in. This soldier and who ever falsified the document should be reprimanded and given an article 15 for this individual is unbecoming and NCO.
NCO Creed
No one is more professional than I. I am a noncommissioned officer, a leader of Soldiers. As a noncommissioned officer, I realize that I am a member of a time honored corps, which is known as "The Backbone of the Army". I am proud of the Corps of noncommissioned officers and will at all times conduct myself so as to bring credit upon the Corps, the military service and my country regardless of the situation in which I find myself. I will not use my grade or position to attain pleasure, profit, or personal safety.

Competence is my watchword. My two basic responsibilities will always be uppermost in my mind—accomplishment of my mission and the welfare of my Soldiers. I will strive to remain technically and tactically proficient. I am aware of my role as a noncommissioned officer. I will fulfill my responsibilities inherent in that role. All Soldiers are entitled to outstanding leadership; I will provide that leadership. I know my Soldiers and I will always place their needs above my own. I will communicate consistently with my Soldiers and never leave them uninformed. I will be fair and impartial when recommending both rewards and punishment.

Officers of my unit will have maximum time to accomplish their duties; they will not have to accomplish mine. I will earn their respect and confidence as well as that of my Soldiers. I will be loyal to those with whom I serve; seniors, peers, and subordinates alike. I will exercise initiative by taking appropriate action in the absence of orders. I will not compromise my integrity, nor my moral courage. I will not forget, nor will I allow my comrades to forget that we are professionals, noncommissioned officers, leaders!

There are two issues to be addressed . The person giving the score and the one getting it . Take them to the side and tell them up front . Tell them both Ethical conduct is a very important Character trait . Fix it quietly but fix it and walk away . Then trust them to do it but verify . And if they fail to . Then it becomes your ethical dilemma . Report it or not . But remember you gave them a chance to do the right thing . And they didn't . But if they do correct it They did the right thing and that's a leaning experience worth Giving them the benefit of a doubt for a momentary laps of judgement . And no more needs to be said or done . Nor should it be held against them . in any future dealings

You need to do the right thing, it is not on you, all those other NCO’s should have done the right thing in the first place, you need to speak up and up hold the core values of the US Army. Their lack of judgement and your becoming aware places your career in jeopardy. Just my 2 cents worth

It sounds like she’s using her feminine qualities to keep her career moving. My advice would be to get in on the action.