In 1884, Germany formally took possession of the northeast quarter of the island and it became known as German New Guinea. In 1884, a British protectorate was proclaimed over Papua -- the southern coast of New Guinea. The protectorate, called British New Guinea, was annexed outright on 4 September 1888 and possession passed to the newly federated Commonwealth of Australia in 1902 and British New Guinea became the Australian Territory of Papua, with Australian administration beginning in 1906.

Can we conclude that was papua new guinea ever part of australia?
yes