Praise be to Allah.
This phrase is not correct in its meaning, because Allaah is the Creator of all things, and His is the Dominion, and He is not absent from His creation and Dominion so that He would appoint a khaleefah on His earth. Rather Allaah appoints some people as khaleefahs of part of the earth. Every time an individual, group or nation is destroyed He appoints another as a khaleefah to succeed them (yakhlaf) in populating the earth, as Allaah says (interpretation of the meaning):
“And it is He Who has made you generations coming after generations, replacing each other on the earth. And He has raised you in ranks, some above others that He may try you in that which He has bestowed on you”
“They said: ‘We (Children of Israel) had suffered troubles before you came to us, and since you have come to us.’ He said: ‘It may be that your Lord will destroy your enemy and make you successors on the earth, so that He may see how you act’”
“And (remember) when your Lord said to the angels: ‘Verily, I am going to place (mankind) generations after generations on earth’”
i.e., a kind of creation that would succeed those of His creatures who came before.
From Fataawa al-Lajnah al-Daa’imah, 1/33
Al-Nawawi (may Allaah have mercy on him) said in his book al-Adhkaar:
Chapter on words that it is makrooh to use.
The ruler who looks after the Muslims’ affairs should not be described as the “khaleefah of Allaah,” rather he should be called the khaleefah (caliph), and the khaleefah (successor) of the Messenger of Allaah (peace and blessings of Allaah be upon him), and Ameer al-Mu’mineen (Commander of the Faithful, leader of the believers).
It was narrated from Ibn Abi Mulaykah that a man said to Abu Bakr al-Siddeeq (may Allaah be pleased with him): “O khaleefah of Allaah!” He said, “I am the khaleefah of Muhammad (peace and blessings of Allaah be upon him), and I am content with that.”
And a man said to Umar ibn al-Khattaab (may Allaah be pleased with him): “O khaleefah of Allaah!” He said: “Woe to you, you have gone too far! My mother called me ‘Umar, so if you call me by this name I will accept that. Then I grew older and was given the nickname of Abu Hafs, so if you call me by this name I will accept that. Then I was appointed in charge of your affairs and they called me Ameer al-Mu’mineen, so if you call me by this name I will accept that.”
The imam and great qaadi Abu’l-Hasan al-Maawirdi al-Basri, the Shaafa’i faqeeh, stated in his book al-Ahkaam al-Sultaaniyyah that the imam (ruler) may be called a khaleefah, because he has succeeded the Messenger of Allaah (peace and blessings of Allaah be upon him) in ruling his ummah. He said: So it is permissible to call him khaleefah, or the khaleefah of the Messenger of Allaah.
He said: But they differed as to whether it is permissible for us to call him the khaleefah of Allaah. Some of them said it is permissible because he implements the laws of Allaah among His creation, as Allaah says (interpretation of the meaning): “He it is Who has made you successors generations after generations in the earth” [Faatir 35:39]. But the majority of scholars said that this is not allowed, and they counted the one who says that as being among the wrongdoers. This is the view of al-Maawirdi.
End quote, from the words of al-Nawawi (may Allaah have mercy on him).
And Allaah knows best.