Then a crash course for you:
FHQ gives damage and resistance buff to infantry in proximity.
If you attack frontally units near FHQ without sniper, mortar or HMG support you WILL be murdered mercilessly.
Take out FHQ first with stuka, ISG or mortars, then conscripts will loose their buff.
The properly described problem includes solution within itself, now we know you didn't meant/knew that, which was already accurately suspected earlier.
The conclusion is, it have absolutely nothing to do with conscripts as expected.
As he said those are all good counters, You can also flame it down with pio (HMG pin is a must for this to work) or a flametruck. 2x flame pios flame crit buildings pretty fast.
Assault nades from OKW and Wher can work as well depending on building strength.
And last but not least you can crush it with any tank.