You didn't include the Persian spelling as it uses the Arabic script.
Persian مسلمان The language does not usually have the vowel marks so you learn pronunciation by memory. For your edification there is a 'o' sound over the 'm' م and an 'ah' sound over the 's' س.
In Urdu, which also uses the Arabic script as well, it is مسلم. The pronunciation is closer to the English Moslem. This is transliteration into another language and it's not perfect.
Stop showing off.
Anyhow you need to broaden your research.
American Moslem Foundation / House of Mercy Project
Why Do People Say Muslim Now Instead of Moslem? | History News Network
So, I regret to say my timeline is also correct.