That quote doesn't contradict what mkl said, towards the end of the article it does say this thou, "The cloak will be on display in the new museum developed in Perth, set to open in Spring 2024."

As your quote says, the conservation work was a collaboration. The cloak itself has since 1842 been in the possession of organisations in Perth, Scotland, the most recent of which asked the British Museum and Te Papa to help restore it, and it will now be loaned to the British Museum. It has not been in New Zealand in nearly 200 years, so has not ever been in our national museum, Te Papa.