Going through migration at connecting flight airport [closed]

The question is not really clear, in any case:

Forget the notation of countries and country boundaries. These are mostly irrelevant (and so many exceptions), but people think about them as correct delimitation of laws.

There is a "Schengen Area" and "country custom area". So you are inside or outside such areas, and only this matter.

To enter and exit Schengen Area, you need to pass immigration. On internetional airports (and international ports) there is usually an area within Schengen and an area outside Schengen. On such structures, the delimitation of both area (and with other restricted area) are clearly marked.

As you stated, both Frankfurt and Amsterdam (the cities) are inside Schengen area, so airplanes will depart and arrive from the Schengen area of the terminals (and the airplane is considered as inside Schengen area). So you need to enter in Frankfurt to the Schengen area, but in Amsterdam you are already in Schengen area.

Note: Schengen area is not a geographical area: You will see it e.g. in Frankfurt: the trains connecting terminals will use the same rails, but you can be either inside or outside Schengen. The relevant doors opens only on the correct area. So you will not accidentally pass from an area to the other. Taxi way and runways are similar: there is a control that people will not mix up between areas (e.g. when you go to an airplane by walking or bus+walking).

Note: Wikipedia articles of Schengen area has a list of territories excluded from Schengen area (but within France, Nederlands, Spain, ...). Boundary zones are also special: you enter Schengen after immigration, which could be done on shore (and not in the middle of a bridge), near the first village (and not in the pass, when state boundary is in mountainous regions), and, as above, airports and ports have distinct areas. Custom areas are much more complex and with many other exceptions.

All the people on any plane must be either inside or outside the Schengen area. Otherwise, arrival would be a logistical nightmare, because it would be difficult to keep track of who was where for immigration purposes.

If you were going through immigration in Amsterdam then so would all the other passengers, which would mean that everyone flying from Germanyto the Netherlands would have to go through two passport checks. That's obviously contrary to the purpose of the Schengen system.

The point is not to allow connecting passengers to avoid immigration controls, but to allow internal passengers to avoid them. This means that connecting passengers go through the passport check only at the points of entry into and exit from the Schengen area.

TL/DR:

FRA was your point of entry into the Schengen area which is why you cleared Immigration there.

FRA-AMS is domestic for Immigration purposes as it's wholly within the Schengen area.

No. You have already cleared Immigration in FRA. While member states retain the right to have border controls, The Netherlands does not at this time.