What can I do if one of my referees falsifies information in a Letter of Recommendation?
This is a most unusual situation. It's extremely rare for there to be such a large discrepancy between what a student thinks a professor thinks about them and what the professor actually thinks about them. Considering also that in this case the professor's opinion is wrong (as I will assume for the purposes of the answer, though I know nothing of the details of course), this scenario falls right through the cracks of the whole system of letters of recommendation, which was simply not designed with such situations in mind.

With that said, I think that somewhat ironically, the very strangeness of the situation offers a glimmer of hope, since it means that you can consider unusual steps that would not be acceptable in a more normal situation. Specifically, two such steps that I can think of are:


You could write a letter to the schools to which you applied (specifically, email it to the admissions committee, and make sure to cc a staff member and ask for an acknowledgement) in which you explain the situation. If your letter is well-written and the explanation that you offer is credible, this may counter the effect of the hypothetical damaging letter from the professor. You may want to line up another letter writer in advance of sending your letter to substitute for the bad one.
You could complain about the professor's behavior to the department chair or another professor you trust at your university, explain the details of the story, and ask them to write to the schools you applied to. This would not be a normal letter of recommendation. It should be an email sent directly to the admissions committee (rather than uploaded via some kind of automated system for LORs), again explaining the situation. Having the explanation come from the chair or another faculty member, if they agree to do it, will be more credible and increase the chances of success. In fact, the chair may very well know of similar stories of odd behavior involving your professor that you were not aware of, which he could mention or hint at in his/her letter, further strengthening the credibility of your claims.


Note that in both of these suggestions you will have to disclose all the information about what took place between you and your professor to make the explanation credible and have a realistic hope that the professor's false accusations will be ignored. If some of what took place is embarrassing or damaging to you due to real rather than imagined reasons, I'm afraid that's just a risk you'll have to take. Good luck!