Another answer from our community:
The claim is simply justified by the fact that Islam (as an Arabic word) in its universal sense means submission to God. All God creatures were created on submission (Islam) to God. They have no choice rather than submission (Islam) to God. However, on mankind creation they were given the choice to do the good or the bad, to maintain full submission (Islam) to God as the one and only one God or not. Accordingly, over history, God assigned his prophets to call their people to Islam (submission to God) with no partner and no associate. Muslims believe Islam is the real mission of all God prophets; including Noah, Abraham, Moses, Jesus, and Muhammad (peace be upon them all) and all their followers are Muslims. However,
Logic justifies a claim that those who worship the Abrahamic God give submission ('Islam', in Arabic) to their God, but it would be a misuse of logic to say that they were in some way members of the Islamic faith - except, of course, the followers of Muhammad.
In the ordinary sense of the word, those prophets and followers who considered themselves Jews were Jews; those prophets and followers who considered themselves Christians were Christians; those prophets and followers who considered themselves Muslims were Muslims. We can not change this retrospectively, after many centuries.
From a non-Islamic viewpoint it may be seen as disingenuous.
Hinduism
The Muslims believe that Hazrat Muhammad SAW was the last prophet of Islam. Some people like Museelma Kazzab ( the lier) claimed to be prophets but the Muslims fought against such false claiments of prophethood during the reign of the First Rashidoon Caliph Hazrat Abu Bakr Siddique RAU. All such prophets were defeated and killed by the Muslim army under the command of Hazrat Khalid Bin Waleed RAU. Thus all the people who claim to be prophets after Hazrat Muhammad SAW are considered False by the Muslims. Mirza Ghulam Admad and his followers are not considered Muslims. If some ahmadi ( a foolower of mirza ghulam ahmad qadiani) tries to perform Hajj and is discovered by the Saudi Govt., he is put behind the bars. However, the Ahmadis claim that only they are the Muslims.
Islam is the religion, Muslims are the followers. Some people claim to be Muslim but murder and oppress others for money, power, etc., or have wrong ideas about Islam and think such actions are permissible. However, one cannot judge a religion by the actions of some of its followers, or else every faith would be guilty of hideous crimes. The reality is that Islam forbids violence except in self defense, and most Muslims abide by that.
Christianity prophets are people who claim they can speak to God. Examples would be Moses, Jesus, and Noah.
The Muslims and Jews both claim that Palestine is their land at that they have been living there for thousands of years. The Muslims do not have any proof of their claim, but the Jews do.
Yes there are false prophets, people who claim to be prophets, when they are really not sent or called by God.
Muslims usually reject this claim and say that Allah guards only the Quran.
It is worth noting that Muslims claim that the Islamic Establishment did not write any of Islam's Holy Books. They attribute authorship entirely to God through acts of revelation to prophets. Islam's chief holy book is the Qur'an.
We do not know the meaning of life, so that claim cannot be justified.
No true prophets claimed to be the Messiah other than Jesus Christ himself. False prophets may have claimed to be the Messiah, but no true prophets of God ever made such a claim.
So they can appeal to Christians (and other people) and get more followers.
Abou Bakr Assidiq was elected by Muslims as prophet Muhammad (PBUH) successor of the prophet death.