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.
People who need to lie about obtaining any title are clearly not capable (or not able, maybe for external reasons) of obtaining said title (otherwise they would have done so), but want to enjoy the benefits that come with this title. By not being capable of earning the title (in most cases), the person is not displaying the required traits of those who successfully (through hard work) earned that title, which, in my opinion, gives a bad name to all holders of that title.
There are, of course, some people who have earned a PhD, but still give other PhD title holders a bad name, but it is their right to do so, they have earned the title.
Those who did not do the hard work and did not earn the title do not have the right to do so and need to be reported without exception.
When reported, it should be reported to the ethics council of the university the fake title supposedly came from or the the ethics committee of the Ministry of Education (or similar).
Yes, of course report the situation.
If what you describe is accurate, there is a high likelihood this person committed serious fraud (i.e. mail fraud or wire fraud) as a 'semi-government company' (particularly in the US) is very likely to have required multiple forms of proof of graduation. Federal jobs, for example, routinely require transcripts, documents, the whole file. Federal contractors follow suit.
For this reason, what you claim here is (to me) quite fantastic and requires you to delineate between 'knowing this person is a fraud' and 'I can't find suitable evidence to prove this person is whom he claims to be'. But certainly this sort of thing happens, I assume.