Munich Airport Customs/Immigration

No you will stay airside so not entering Germany but passing through an airport to Italy.

On the way to the connecting flight you will only go through Immigration in Munich where they will stamp the passport. A 1 1/2 hour connection time is sufficient otherwise the airline could not sell you the ticket that way. If your flight from JFK is delayed causing you to miss the connection the airline will put you on the next flight with available space to Rome. The last one on Lufthansa leaves at 19:25.

Ah good. Same as they do in Tokyo. Thank you

You will go through Schengen Area immigration (passport control) in Munich. You will not go through passport control in Florence as both Germany and Italy are in the Schengen Area.

As this is one booking, your bags will be labelled through to Florence, and you pick them up there.
After you have picked them up (in Florence), you walk through customs (luggage check), through the "nothing to declare" green door. This is a random check only, 95%+ of travellers just walk through without stopping.
No customs in Munich as you will not see your bags there.

you will stay airside so not entering Germany but passing through an airport to Italy.

"not entering Germany" but entering the Schengen zone, so there will be immigration (passport check).

According to the Lufthansa website for today, the flight from JFK will arrive at an 'L' gate in the new satellite gates of Terminal 2, and the flight to Rome will leave from a 'K' gate, also in the satellite terminal. The K and L gates are on different levels, 4 and 5, respectively, but it looks like the L gate where you arrive will be configured to send you up to level 6 which is for non-EU arrivals. You'll have to go down 2 levels to the K (Schengen) gates, and somewhere along the way you will go through Schengen immigration.

There is no guarantee that the gates letters will be the same when you arrive, but you can check them on the Lufthansa website.

There is a small chance that you could be arriving at an 'H' gate. No problem if the flight to Rome leaves from a 'G' gate. Those gates are in the old Terminal 2 building (H on the 5 level, G on the 4 level) and the routing is similar to the satellite - you go through immigration between levels.

If it turns out that you arrive at an H gate and depart from a K gate, or arrive at an L gate and depart from a G gate (hopefully you won't) then you will have to transfer between the main Terminal 2 building and the satellite. I think there is a shuttle train between the buildings, but I don't know anything else, like whether it's entirely within the security zone or whether you will have to go through security when changing terminals.

Perhaps someone, like SLA019 can add more information.

Thank you Lee, that is good information. At least now I know what to expect. After looking at the link you provided, I see that there are 5 flights to Rome so we should not have any problem. Actually, would not mind spending an evening in Munich. We haven't been there since 1975.

I think there is a shuttle train between the buildings, but I don't know anything else, like whether it's entirely within the security zone or whether you will have to go through security when changing terminals.

Yes, there is a shuttle train (for just 400 meters!) and you stay airside. The only access to T2-satellite is through Terminal T2. Immigration is in T2-satellite (from the US: level 05 ("non-Schengen clean").

(If you read German, you can find an extensive description of T2-sat here).

Interesting. What countries are considered NOT "non-Schengen clean" (is that non-Schengen "unclean")? I think I read that Terminal 2-main has added a 6th level for passengers coming from those countries.

Do flights coming from the US allow passengers to go directly to level 5 in T2-satellite, or is all of immigration (not just unclean) in level 6 of T2-satellite.

EDIT: I guess one of your links explains all that.