PhD project ownership conflict after changing university
For what it's worth, I don't think either university can own the project directly. Anybody can work on anything, pretty much, but there are many caveats. If code or data were produced, that may be owned by UniA. If there was funding, it's definitely going to stay at UniA. So you may have to find some alternative source of funding to work on the project, but if the supervisor at UniB wants to pay you to work in the same area, you almost certainly can. Now, if you can't come to agreement with the supervisor at UniA, you may also have some trouble publishing when it comes to things they wrote. It would be best to get the two supervisors to come to an amicable agreement to work together on it with you at UniB.