That's a terrible idea. You've now coupled your tests to someone else's code.
Test the endpoints separately. Wrap the endpoints to allow you convenient dependency injection. Test the wrapper. This wrapper is ideally a very thin layer of boilerplate, that you won't ever touch very much, and shouldn't take much time to write or test.
But this is the key, however: use the data specifying the expected outputs of your third party API as input parameters to the test of the wrapper, and expected outputs from the wrapper as parameters for your integration tests. Keep each set of data in one place, so that changing it for one test, changes it for the others.
By using shared test datasets in this way, you prevent modules from getting out of synch with each other, and can still replace/update parts in separation.