Ms Lini is the daughter of Walter Lini, who is known as the founding father of the Pacific nation.
The United Liberation Movement of West Papua has welcomed the move with spokesperson Jacob Rumbiak saying they are pleased and impressed and thank Vanuatu Foreign Minister Ralph Regenvanu for the appointment.
"Melanesian sovereignty runs deep in the veins of all ni-Vanuatu, and especially in Laura's family," Mr Rumbiak said.
"In the 1970s both West Papua and Vanuatu were struggling for their independence.
"Vanuatu got there first and it was Laura's father, as Prime Minister, who pledged not to abandon West Papua or the Kanak of New Caledonia," he said.
Mr Rumbiak said there was now just one more river to cross before West Papua rejoins the international community of nations, and that is to be listed on the UN Decolonisation Agenda.