If Craig Wright has a PhD you should be able to find his dissertation, look up his advisor/thesis committee, see his publications in CS conferences, etc.
https://researchoutput.csu.edu.au/en/publications/the-quanti...
Wright, C. (2017). The quantification of information systems risk: A look at quantitative responses to information security issues Australia: Charles Sturt University
Doctor of Philosophy
I suspect he may very well have considered himself 'basically done' with his PhD several years ago and just started using the title. He wouldn't be the first
A few weeks before bitcoin's release: https://archive.is/Ao7DQ
"Many 2-year community colleges often hire instructors with only master’s degrees, as long as they have some teaching experience. Four-year colleges and universities usually require a doctoral degree, unless you have decades of experience in your field, in addition to a master’s." http://www.teachingdegree.org/types-of-teachers/higher-educa...
That said, I don't actually doubt that the SGI letter exists, but also believe it was totally fabricated by Craig Wright.
https://www.reddit.com/r/Bitcoin/comments/3w8efk/wikileaks_s...
Here's some information class about he was teaching right until they scrubbed it: https://web.archive.org/web/20120430035605/http://www.itmast...
And another: https://archive.is/ttLth
This was on their youtube page: https://archive.is/gXPkX "Presented by Dr Craig Wright of Charles Sturt University and the Global Institute for Cyber Security + Research."
The SGI endorsement letter existed. I have a copy, but the web version was scrubbed. The remaining evidence is in the form of a copy of press release http://archive.is/cqI6S