Flight instructor with student on training flight reported a NMAC with a helicopter while in the traffic pattern of a non-towered airport.

Narrative

I was working on flying traffic patterns with a flight student pursuing his Private Pilot certificate. We were currently in the right downwind for Runway XX at ZZZ. While we were established in the downwind; just north west of the airport; a Robinson R-44 helicopter quickly appeared from the south east and flew directly over the airport and crossed just in front of; and above us. When we saw him there was no time to take evasive action.Right after we landed I spoke with Person A; the airport manager. Person A pulled up an ADS-B tracker on the office computer and saw the track of the incident. When he selected the aircraft; no tail number was given. It just displayed the type as an R-44; that they were 1100 feet (traffic pattern is 1028); and that they basically passed right above us. According to Person A; the details showed that is had departed ZZZ1 and was going to ZZZ2. In an attempt to get the tail number; I called the Tower at ZZZ2 and was told that a R-44 had not landed there. I attempted to call the ZZZ1 Tower; with the number given to me by the ZZZ TRACON and it kept disconnecting.