Anthony Maslin and Rin Norris yesterday thanked Ms Bishop for "everything she has done for us", telling The West Australian the former foreign minister had held Russian Federation to account for their involvement in the "catastrophic tragedy" of MH17.
Morrison emerged as the surprise victor of Friday's party-room vote to replace Turnbull after a week of political chaos in Canberra that marked the emergence of Australia's sixth prime minister in less than 10 years.
The City of Sydney councillor said she had a strong record of championing Liberal Party values at a local government level.
New prime minister Scott Morrison, who won the leadership ballot against Peter Dutton, is weighing up his new ministry to reunite the Liberal party.
Morrison, the former treasurer (finance minister), was sworn in as prime minister on Friday after winning a Liberal Party leadership challenge against incumbent moderate Malcolm Turnbull.
Speaking to The West Australian, an emotional Ms Bishop ranked her fight to win justice for families who lost loved ones in the on MH17 as among her greatest achievements, and urged her successor to continue to pursue Russian authorities.
"Cormann rumoured to be putting some WA votes behind Julie Bishop in round 1", a message assumed to be sent from Infrastructure Minister, Paul Fletcher read.
Ms Bishop's Labor counterpart Penny Wong paid tribute to her for her trailblazing role as the first Australian woman to be foreign affairs minister.
Pakistan bans first-class air travel by PM, president, govt officials
That may surprise some of you, but they had a good call. "They (Pakistan) are an important partner". The prime minister will also not use special planes for foreign visits or domestic travels.
'But she has earned, absolutely, the respect of foreign ministers around the world, ' Mr Rudd said.
There is speculation she could become the next Governor-General, but Ms Bishop is yet to address the rumours.
Tony Abbott has stared down calls for him to retire from public life but has cast doubt on the offer from the prime minister, Scott Morrison, to make him the special envoy for Indigenous affairs, questioning whether it is a "fair dinkum" role.
The possibility that Ms Bishop could leave Parliament before the next election will be a major concern for Mr Morrison, Mr Turnbull's former treasurer, because it opens the possibility of another by-election being held for her seat.
"You have to have inexhaustible supplies of energy to be a federal politician from Western Australia anyway". "What I'd like to know from Scott is exactly what he's got in mind".
She may be Australia's first female foreign minister and has been the most senior woman in Cabinet for years, but she has resisted being defined by her gender.
'Ms Bishop's commitment to standing up for Australia both here and overseas has been been in question, ' her statement said.