Is it permissible for the mu'adhdhin to leave the mosque after the adhan?

Q: A. M. J. from Riyadh asks in his question: Is it permissible for the mu'adhdhin to leave the mosque after raising the adhan for some need, such as having guests whom he wishes to see off, and then returning before the iqamah of the prayer? And is it permissible for him to raise the adhan while not in a state of ritual purity, and then go out to perform wudu'? Please give us a ruling, and may Allah reward you.

A: It is permissible to leave the mosque after the adhan for a sudden need, such as wudu', or for the need mentioned by the questioner, provided he returns before the iqamah. It is not permissible to leave after the adhan for one who does not intend to return, except for a valid legal excuse. This is based on what is established from Abu Hurayrah (may Allah be pleased with him) , that he saw a man leave the mosque after the adhan and said, "This man has disobeyed Abu al-Qasim (peace and blessings be upon him)." Muslim narrated it in his Sahih.
The scholars understand this to apply to one who has no valid legal excuse, in accordance with all the evidence.
It is permissible for a Muslim to call the adhan while not in a state of ritual purity and then purify himself afterwards, but his adhan is better if he is in a state of ritual purity. This is based on what was reported from the Prophet (peace and blessings be upon him) that he said: However, its chain of narration is weak.
However, it can be inferred from this that wudu' is better before calling the adhan if it is easy to do so. The same applies to tayammum for one who is unable to perform wudu' due to illness or the absence of water.
And success is from Allah.