Should I inform authorities of someone falsely claiming a non-existing PhD?
It is certainly appropriate for you to bring this to everyone's attention. However, it is also important that you do so in a way that will protect yourself from retaliation as you seem to suggest the person has some power. 

The dilemma, of course, is that an anonymous accusation is easy to dismiss. But if you can just direct people to source of your information so that they can independently verify your claim it will stand a better chance of being heard. 

It is also possible, that the "authorities" are already aware of this and are, in fact, invested in the career of the person. This happens in some places, so, depending on the norms of your location, it may be especially important to protect yourself, and in the worst case prepare for the situation that it won't be addressed.