First of all, it's important to note that this answer is relevant to United States law, and shouldn't necessarily be taken as legal guidance, more-so a path of reasoning out a solution that may be applicable to you depending on your country etc.
If they choose to actually report the fake evidence to the authorities, you should look into having the police check their call history with their phone service provider, as well as yours. I'm aware of online phone services on the web and through apps that could potentially be used for this kind of thing. Make sure to let the appropriate people know that this is a possibility, in which case they may need to check the suspect's internet history on their computers and ISP.
Faking evidence is unlawful and if you would like, you might could press charges and potentially solve your problem.
Some helpful links below -