Is the spare sub passive?
Then it's not likely that there will be enough power to drive it and the original sub together. You might damage the main unit of the HTS. You could try using the better of the two alone. Using two different subs isn't better just maybe louder.
If the spare is active then you would need to use a speaker to line level converter. You would have to cut the original cable to connect the converter. That would feed the active subwoofer. Again use the better subwoofer rather than both.