Is it allowed to publish an explanation of someone's thesis?
Properly credited, posting a piece that fills in all the details of a published paper (or thesis) should be fine. Indicate clearly that  the ideas are not your own - that you are just hoping to help others read the original work.
You should probably write the person who did the original research, thanking them for their theorems and telling them what you hope to do with your work filling in details. They will probably be delighted that someone has read their thesis.