The plastic drum and cable unit clips in to the back of the controls,but you need to get the alignment correct.There should be a detent in the plastic to help you.Perhaps the cables have come off at the heater end?.Same arrangement,just clips in once aligned.

Your response has reassured me that it's actually capable of being reconnected (and without the use of a special tool?). Thanks to your response, i'll try again but with a newfound confidence. Thank you!