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In English there have generally been four terms used: Muslim, Moslem, Mohammedan and Musselman. While technically none of these violate any rules of English grammar, Muslim is to be preferred. Most spell checkers will not correct the first three terms.

From the journalism guide “Reporting Diversity,” page 19:

Is it correct to write Muslim or Moslem?
Muslim is preferred. People refer to themselves as Muslims. Many regard Moslem as a term of abuse, like people of African descent dislike being called negroes. Also avoid Mohammedan and Musselman.