We are travelling to Dusseldorf next April have booked tickets from Singapore Flight LH791 to Dusseldorf which takes us through Munich. The flight has just been updated - arriving now Munich at 05:50am and the flight to Dusseldorf is LH2002 at 06:30am to Dusseldorf? Do we have time to transfer the agent suggest okay?
It sounds tight-ish but doable. Munich airport is usually spoken of as extremely efficient for connections -- the minimum connection time for Lufthansa international-domestic is just 30 minutes. They consider this swift connection a definite selling point, and they go to quite some effort to keep it, including such things as proactively fast-tracking late arriving passengers past the lines. Though you're of course always sensitive to immigration delays.
The good news then is that Lufthansa will be responsible for rebooking you if you miss the connection. And Lufthansa fly a lot of direct flights from Munich to Düsseldorf. On the random Wednesday in January I searched for, there are flights departing at:
06:30, 07:30, 08:00, 08:30, 08:45, 09:30, 10:30, 11:30, 13:10, 13:30, 15:30, 16:30, 17:30, 17:45, 18:00, 18:30, 19:00, 19:30, 20:45, 21:30
No matter how long you're held up for at immigration, there will be a flight leaving for Düsseldorf quite soon afterwards that they can put you on.