It's either Muslim or Moslem, Justa Picker. That is because the audible sounds are being translated from a language with a completely different alphabet. Accordingly, the listener decides arbitrarily how to spell it in English characters. You find this with Chinese and Japanese words too, when they are transcribed into English.

Do you spell it Feng Shui...or Fung Shway...or F'ng Shuei...or????

Well, that's up to you, isn't it? Feel free to use Muslim, Moslem, or whatever spelling you prefer. The same seems to go for: Yusuf, Yusef, Yusif, Yussef, Yussif, Yusoof, etc.... (grin)

Totally arbitrary, I assure you. If someone tells you there's only one right way to spell such a word in English, well...that's their opinion...and opinions are as common as grass.