What is the ruling on placing a sign on the mosque's minaret with "Allahu Akbar" written on it instead of the crescent?

Placing a plaque on the minaret bearing the name of Allah, or something from the Qur'an or Hadith, is impolite and exposes it to disrespect. As for placing a crescent on the minaret, if it is for seeking closeness to Allah and an act of worship, then it is an innovation (bid'ah). However, constructing a minaret is desirable for a practical benefit, such as amplifying the voice and distinguishing the mosque. In summary: there is no harm in building a minaret without extravagance, and nothing should be placed on it, neither a crescent nor a plaque bearing the name of Allah.