the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
There is a hadîth to indicate that the person who calls the adhân (the main call to prayer) should also call the iqâmah (the second call to prayer).
It has been related that the Prophet (peace be upon him) said: “Whoever offers the adhân should be the one who to offer the iqâmah”. [Sunan al-Tirmidhî (199), Sunan Abû Dâwûd (514) and Sunan Ibn Mâjah (717)]
However, this hadîth is weak. It has been declared weak by numerous hadîth scholars, including al-Albânî. Therefore, it cannot be used as evidence that the same person should call the adhân and iqâmah.
In any event, even if this hadîth had it been authentic, it would merely have indicated a preference. It certainly does not indicate an obligation that the one who offers the iqâmah must be the same person who had already offered the adhân.
It is permissible for anyone to offer the iqâmah. In the case of your mosque, the mosque's officials can set down certain policies to prevent confusion or hard feelings. Whatever policies the mosque administration sets down should be respected by all. Therefore, if the administration makes it a rule that the iqâmah must be given by the same person who had already offered the adhân, then this is what should be followed.
And Allah knows best.
Source: Islam Today