Munich Airport Transfer Time Enough for Passport Control/Customs?
 

I am trying to figure out if we need to go through immigration/passport control and/or bring our baggage through customs in Munich airport when we transfer through there.
We are flying Lufthansa from Krakow to Munich arriving Munich 14:30 then transferring to a Lufthansa flight from Munich to Berlin that departs Munich at 15:10. Both flights are in Terminal 2 but there's only 40 minutes time between flights.
1) I assume Lufthansa will forward the bags all the way through since we are Star Alliance Gold but does anyone know whether we will have to pick up our bags in Munich and go through customs then redeposit bags for the flight to Berlin? And if so, how long will that take.
2) Likewise, will we have to go through some kind of passport control on arrival in Munich prior to transferring to our flight to Berlin?
We were hoping that since it was all within Europe and we are staying in same Terminal that we could just hop off in Munich then pop over to gate to our next flight.
Otherwise seems like we may be in trouble to make the connection.
Thanks!

There's neither Customs nor passport control on this journey.

Merchandise movements within the EU aren't subject to control (that's the whole point of what most us call the Common Market) and both Germany and Poland are in the Schengen area, which means usually no passport control.

You write in American. Look on this as a flight from New York to Dallas, changing at Atlanta.

BUT:

Munich doesn't have enough jetways for its flights. It's quite possible you'll get bussed into a terminal, then bussed back out to your connection. This is terrifying if you're on a tight connection, but it works. If it doesn't, LH will just put you on the next available flight. There are loads to Berlin.

Thank you very much flanneruk. That's a relief to hear.