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Praise be to Allah.
Firstly:
The imam does not have the right to oblige you to do what you have mentioned, when he is an employee like you and has no authority over you in this regard. You have to refer the matter to the Mosques Department.
Secondly:
It is not permissible for the muezzin to take a salary for giving the adhaan and not do it. By the same token, it is not permissible for the cleaner to take a salary when he does no work; it is not sufficient to hire someone else to do his work without checking with the government department and getting permission from them.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Some people who are employed as cleaners in the mosque will hire a foreigner for one quarter of what they take as a salary, and consume the rest without doing anything in return -- Allah forbid. Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said that such actions come under the heading of consuming people's wealth unlawfully. Some of the directors of Awqaaf departments say: It does not concern us who does the job; rather what matters is that the work is done. I asked the representative of the Ministry about that and he denied it, and said that the Ministry does not approve of it. But it is essential to differentiate between cases where the hired worker is sponsored by the (Saudi) cleaner, in which case it is permissible for him to give him his job, and cases in which the cleaner is not sponsoring him, in which case it is not permissible.
End quote from Thamaraat al-Tadween
What you have mentioned in your question is worse than that. The (Saudi) cleaner is not hiring a worker from his own money; rather he wants someone else to pay the cleaner. This is a kind of injustice and consuming people's wealth unlawfully, as he is taking the salary without doing anything in return. We ask Allah to keep us all safe and sound.
And Allah knows best.