What is the ruling on the imam being 40 minutes late for the prayer, and what is the ruling on the muezzin's statement "Patience, and speak to the imam" to those who criticize that?

The basic principle is that the prayer is conditioned upon the Imam's permission. The muezzin has authority over the adhan (call to prayer), and the Imam has authority over the iqamah (call to commence prayer). The muezzin does not call the iqamah except with the Imam's signal. The Imam should not burden the congregants by delaying, and should hasten to prayer with tranquility and dignity. This applies to both the Imam and the congregants.