What would you do if you knew a MAJ submitted a fraudulent DA Form 705 APFT & DA Form 5500 Body Composition in a packet?

I've called out NCO's and Officers on suspicious documents before. One Senior NCO wanted me to sign off on his 2-1 and 705 for an upcoming board. I looked at his 705 and couldn't recognize who supposedly signed and initialed his test. When confronted about it he kind of changed the subject and went to someone else. I brought this to my commands attention but unfortunately they did nothing about it. This Soldier has never taken an APFT with the unit but someone manages to get updated scores in DTMS and although he has a bigger stomach then Santa Claus he consistently manages to pass his tape. (By a good margin too). I make a point to take a test with my unit so that there can be no perception of bias.

I once had my 1sg tell me to put in medpros that I have her an immunization that I hadn't given her. When I told her no, she asked why. I told her my integrity wouldn't let me lie like that. Six months later I went off on an NCO while off duty. When he told her he wanted me to get an AR15 for disrespect, she told him I must have had a good reason because I had more integrity than anyone she'd ever met. She called me into her office to ask my side of the story. When I told her what was going on she launched an investigation that ended up with that NOV in Levenworth. Lack of integrity in anyone wearing a uniform pisses me off.

She shouldn't be able to go. She is an integrity violation. She was selected falsely

This is clearly UNSAT. Nobody in this forum will say that this is what right looks like.
Complicating things is her rank and ability to imply difficulty on the (almost certainly) lower ranking members that administer the test and record-keeping. I have little doubt that the Major has done this before, and gotten away with it before.
The solution is oversight. When my unit conducts an APFT of any sort, I am out there too. Maybe (usually) taking the test, sometimes as the NCOIC or a grader, but present. When the data gets entered into DTMS, I review it. When the counseling for failures happen, I am involved. When the Flags happen, I make them happen with the S-1 shop. No one is putting in a fraudulent APFT on my watch, and if for some reason it happened, I would likely catch it and certainly know who the enabler would have to be.
This Major is getting away with this because the Sr NCOs allowed it to happen due to their inattention. If known and tolerated, the whole herd needs to be thrown out on their ear.
This officer will command and have to hold accountable Soldiers that fail to meet the standard. By compromising on this, she is no longer fit to wear those Oak Leaves.
Sayanara.

Lose their shot records

It sounds like dereliction of duty on all parts. I have witnessed this before while on AGR status for the PA National Guard Recruiting and Retention. I did not make a scene but I did go through my team leader and he challenged my integrity. Me being a combat vet told the said team leader in the most respectful manner you cannot lead behind closed doors. Then worked it up the chain. Ultimately nothing happened but I did my part in reporting it.

Easy fix invite her commander to an APFT and BF weigh in given by reliable senior NCOs, then figure out who signed her 705s hold all them responsible

CSM, I actually had a conversation about something similar to this subject today. First, I believe there are many senior NCOs and Officers who haven't taken an APFT or weigh and tape in years. You can look at a lot of these 1SGs and CSM/SGM, and a lot of Majors and above who clearly look overweight. I work in many HQs, and can say for a fact that I have noticed many in my day who have never showed their faces at an APFT or weigh and tape. That being said, it's happening all the time and nobody is monitoring/ tracking it. To answer your question- I think the same thing should happen to that officer as did a SGT (P) in one of my previous units who changed the run time for a brand new LT who had failed. She had a lapse of judgement trying to help a LT who was worried about looking like a dirt bag LT, and she lost everything because of it, and so did he. She and he both were given punitive actions and separated from the Army over it. Im glad I'm not in the position to make serious decisions about someone else's career, but being completely honest, how many Soldiers has that MAJ- when he/she was in command -tossed out into the streets, for failing an APFT or HT/WT? Standards are standards and nobody is above them. Soldiers, officers especially, should always act above reproach.

remove him for whatever he was selected for (I'm AF and gave no idea what AGR is) and that's easily an Article 15 offense.

If I have % proof it is false, he doesn't pass go, doesn't collect 200. I first would confront the Major in person in person to see if he wants to retract it. If not, then I go to the TNG Officer/NCO and present the facts, if nothing, then to the CDR.
I was in the position once as SNCO when my unit was to take a APFT. Everyone was there except the XO. Finally he comes out in BDUs and I state we are waiting for him to get changed. He said he wasn't taking the test. I asked if he had a profile, no he didn't. I then stated he needed to changed. He tried to intimidate me, but I never backed down. The CDR came out, looked at the XO and me as asked what the problem was, I explained. The CDR looked at the XO and told him he either right this minute goes to the TMC and gets a profile or get changed. He went and got a profile.