Maybe he's not entirely wrong.
Or at least, whether he's right or wrong might not be the same as whether you can usefully "make my Muslim friends understand why this is wrong".
A discussion which includes a reply like, "What you said is just wrong! The truth is that etc.", might not go very well in real life, 'human nature' being what it is.
It might be better to have a discussion which includes replies like, "What you said is interesting and there may be some truth in that.", and which then goes on to add to (augment) or shed more light on what they said.
FYI the 'Four Noble Truths' are spelled out in the Dhammacakkappavattana Sutta,
Now this, monks, is the noble truth of stress: Birth is stressful, aging is stressful, death is stressful; sorrow, lamentation, pain, distress, & despair are stressful; association with the unbeloved is stressful, separation from the loved is stressful, not getting what is wanted is stressful. In short, the five clinging-aggregates are stressful.
"And this, monks, is the noble truth of the origination of stress: the craving that makes for further becoming — accompanied by passion & delight, relishing now here & now there — i.e., craving for sensual pleasure, craving for becoming, craving for non-becoming.
"And this, monks, is the noble truth of the cessation of stress: the remainderless fading & cessation, renunciation, relinquishment, release, & letting go of that very craving.
"And this, monks, is the noble truth of the way of practice leading to the cessation of stress: precisely this Noble Eightfold Path — right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration.
You can double-check what the third noble truth says here on buddha-vacana.org site, which has a word-by-word translation (try using the mouse to hover over each word of the Pali), which I could translate as:
- And this surely, monks, cessation-of-suffering noble-truth: that very desire not leaving a remnant dispassion/nirvana cessation abandoning giving up release freedom from attachment.
I think he's saying that giving up desire is the cause of cessation-of-suffering ... or more specifically, not the cause of cessation but the state of cessation -- the truth of cessation, the state of cessation, the reality or conditions in which suffering has ceased, is the state of freedom from attachment.
The fourth noble truth is the practice: it's how to do that.
Your friend says, "when desire is eliminated there is no reason to have a fourth noble truth" -- however, how to practice "desire is eliminated" isn't obvious. Specifically, before the Buddha became enlightened he tried to practice some extreme austerities before deciding that didn't help, and that the Middle Way (and, in more detail, the Noble Eightfold Way) was better, was the way to be taught.
Let me try another simile for the four noble truth:
- A car crash is painful
- A painful car crash is conditioned by (i.e. it happens when there is) uncontrolled speed
- There's truthfully no danger of the pain caused by a car crash, when the car isn't speeding
- The practice for not speeding is to avoid using the accelerator and to use the brakes.
So I think you're friend may or not be right.
If he's saying something like, "I can safely drive a car without brakes, because I won't be driving very fast", perhaps that seems true theoretically, but the problems with that statement ought to be obvious.
If you want to talk with your friend about states of being in which "desire has been eliminated" it might be worth considering this answer too.
I think it says that different schools (or practitioners) of Buddhism may have different ways of living. If you don't mind my saying so (and because you added the comparative-religion tag to your question), there are different branches within Islam too, for example Sufism.
That answer (i.e. what Bhikkhu Bodhi writes about the Mahayana) is probably easy to misunderstand, though, and it isn't the first thing to be learned about Buddhism. I thought the first thing to be learned about Buddhism was the Four Noble Truths (I thought that was the first thing to be taught), but for some second opinions on that, see the answers to How to explain what Buddhism is? ... and note that when Suminda's answer says "three trainings", those three training are actually a synonym for the Eightfold Way, i.e. for the fourth noble truth.
And so, although your friend might say, "there is no reason to have a fourth noble truth", in a sense the fourth noble truth is the practice of Buddhism.