In case there was any doubt, I have asked them. This is the conversation I had with them (some irrelevant parts omitted):
Albert: Hello, I have written a book on Mathematics that I would like to turn into a PhD thesis
Albert: what do I have to do?
Their Guy: What is your highest level of education?
Albert: I have a Masters degree in mathematics
Their Guy: Ph.D degree will cost you $1100.00 (USD)
• 1 Original Accredited Degree
• 2 Original Transcripts
• 1 Award of Excellence
• 1 Certificate of Distinction
• 1 Certificate of Membership
• 4 Education Verification Letters
Albert: how long will it take to complete it?
Albert: I already have the thesis, it is a 300 pages book
Their Guy: When are you planning to enroll?
Albert: as soon as possible
Albert: once the payment and the thesis are sent, how long will it take to have it accepted?
Senior Guy: Alright you have been transferred to senior student counselor
Senior Guy: Shipment Details :-
Senior Guy: 2 set of documents we are going to send you in total in 2 separate shipments.
-First set of degree documents will be sent in just 15 - 20 working days with all 10 degree documents without attestations.
-Second set of documents will be sent in only 25 - 30 working days with complete and comprehensive attestations with all above mentioned authorities.
Senior Guy: Total Fee Submission including all registrations would be $1700.00 USD ( $1100 + $600 )
Albert: how long will it take you to review my thesis?
Senior Guy: Well it will take us 24 Hours
Senior Guy: Forward your resume & thesis on email@example.com
Albert: thank you, you have been most enlightening
So, they are reviewing 300 pages in 24 h (where it should take like a year). They do no checking whatsoever on what I would be submitting.
I am sorry, but you have lost the money.
I have found something funny. The faculty (only visiting faculty seems visible for our university) is the same as, including pictures and order, in another online university and another one and another and yet another one, ¡and even more! (and at least, 5 more, but you get the point); all of them looking equally suspicious.