The 775 km between Hamburg Airport and Munich Airport take roughly 7h 43 by road. Booked as a transfer it is one vehicle from one terminal kerb to the other, at a price agreed in advance — which matters more than usual on a day that has already gone wrong.
The pickup is driven by your inbound flight number: the driver watches the actual landing time and waits 60 minutes free after touchdown, which is what a diverted or delayed arrival needs. At the far end the drop-off is at the correct terminal for your departure — Munich Airport has 2 and the wrong one costs a shuttle ride you do not have time for. Tell us the departing flight at booking and the schedule is worked backwards from its check-in deadline rather than forwards from a convenient departure. We run the same journey to Frankfurt Airport, priced the same way.
Luggage stays in the car for the whole 7h 43, which is the single biggest practical difference from any rail route: nothing is lifted onto a train at Hamburg Airport, off it again at the interchange, or onto a second one for the run into Munich Airport. If the airline has rebooked you and is reimbursing ground transport, the invoice shows the route, the date and the fare in a form an airline will accept.
Checked bags are the whole argument
With cabin baggage only, the rail route between two airports is an inconvenience. With checked bags it is a different journey altogether: every interchange means lifting cases onto a train, off it, up a staircase when the lift is out, and along a platform to the right carriage. A car takes the bags once at Hamburg Airport and gives them back at Munich Airport. A saloon holds three large cases, a van takes seven passengers with luggage to match, and if you are travelling with sports equipment or instruments — the things that make a rail change genuinely hard — say so at booking and the right vehicle is sent.