The problem for me is I dont have enough direct experience with desiccated thyroid to know exactly how much (if even possible) to offset the reduction in synth.
I know the synth pills can be very small wich is going to have a direct impact on ability to cut them but a pill cutter should help.
Honestly if your friend is suffering it may be more trial and error than they can handle so getting professional guidance may be the best way to go.
Otherwise, depending on pill size I would see if they can be quartered or perhaps contact the doc and see if a different size tablet can be obtained. Cutting half a pill at once may be too much depending on how they respond to the synth, this is where the experience of someone who has done this many times will come in.
Wish I had a better answer for you but just too many variables/