The question: Shaykh, he also says: If a person enters the mosque before the adhan and prays the greeting of the mosque, is there a sunnah prayer between the adhan and the iqama?

We say, if a person comes to the mosque and the mu'adhin has not called the adhan, the sunnah is to wait if the adhan is near.

And if he remains standing until it finishes and then prays, because it is established from the Prophet ﷺ that he said: Between every two calls to prayer there is a prayer.

So the sunnah in this is that he prays two rak'ahs without the adhan, if he comes and prays the greeting of the mosque before the adhan, then the mu'adhin calls the adhan.

Then the sunnah is for him to stand and pray another two rak'ahs, and this is also a sunnah, and it is not obligatory on him. And Allah knows best.