Is it permissible for the Imam to announce in the mosque the loss of an item or the finding of a lost object, and was this reported during the time of the Prophet (peace be upon him)?

The statement of the Imam, "Something is lost, whoever finds it, let him bring it," is a public announcement of a lost item in the mosque, which is not permissible, based on the saying of the Prophet, peace and blessings be upon him: "Whoever hears a man announcing a lost item in the mosque, let him say: May Allah not return it to you."

As for the Imam's statement, "Whoever has lost such and such an item, let him contact so-and-so, for it is with him," this is the identification of a found item (luqata). This is permissible at the mosque door or in a circle with a low voice, but it is not permissible to raise one's voice with it inside the mosque. The public announcement of a lost item (inshad al-dallah) did occur in the mosque during the time of the Prophet, peace and blessings be upon him.