Hi
Every touch id sensor is uniquely linked to the iPhone's processor so simply replacing the touch id sensor will cause the phone to loose touch id functionality. You must use the original sensor that came with the iPhone otherwise you loose touch id forever unless if you're willing to replace the iPhone's logic board with one that is linked to a touch id sensor.
During disassembly, you must have either done damage to the touch id sensor or the sensor itself isn't properly installed. There are a number of factors that contribute to its failure. The touch id flex cable could have been accidentally pinched or damaged by lifting up the screen too high or there could have been damage done to the capacitors when removing the sensor from the screen itself. Or the captive screw was not secured in the correct orientation. Or the connector itself isnt properly seated onto the socket. A small amount of people even reported that a restore did the trick however its not very likely that will fix the problem after opening the phone up.
So to answer your questions in short, it is impossible to replace without restoring touch id functionality, you can go through the possible scenarios i listed and check your work and hope that nothing was damaged. A multimeter or voltmeter is always a great tool to have for diagnostics.
Best of luck