Must the muezzin return the salary for the two months in which he was absent from his mosque, knowing that there was someone deputizing for him?

You are required to return the salary for the two months you were absent, unless the responsible authority permits you to benefit from the amount and absolves you of it. It is not permissible for you to be absent and delegate someone else unless you have been explicitly or customarily authorized to do so, because it is a trust. Allah has forbidden betraying trusts and commanded fulfilling contracts.