When a class gets a collaborator from a static factory and it is not feasible to inject the collaborator in normal circumstances you could uses a few different techniques to test or mock the collaborator:
Add a setter to the Factory, this could be called before running a test. This way we could inject a mocked collaborator
Add custom constructor that is only called at test time for inject a mock collaborator
Add a custom Collaborator setter, this setter is never called at run time because the collaborator is created the "normal way" but at test time can be used to inject a mock collaborator.