Converting frozen hash brown patties from oven cooking to stove top
Yes you can do this, but it will add some additional fat to your hash browns.

Pour a tablespoon or two of peanut oil (or veg oil if you prefer) into your frying pan and heat it up.

Lay your hash browns down into the pan, and check the bottom for desired doneness, anywhere from 2-5 minutes depending on the hash brown and the amount of heat you are using. Then flip the over and check for doneness again.

The reason it takes less time this way is because they are being cooked in oil rather than being exposed to hot air. It takes longer for the heat to get to the center of the hash browns in the oven.

However, why don't you just make fresh hash browns. You just shred a potato or few, perhaps some onion as well and just drop the pile into an oiled hot pan heated to low or medium low heat, and flip it once the bottom just starts to burn, again then check when this side is ready.