Is it working correctly with AM?

The defective part is located in the counter box. But it's not any of the known common defects.

One can exclude the display driver AO810 and segment driver AO808 as well as the -12 V supply (LM320K).
You can also exclude MC10116K and 95H90, because you get the wrong frequency in FM and also in AM.

All other ICs and parts in the counter box must be checked according to the service schematics. Also the +5 V supply in the counter box shall be checked.