The culprit is Hatsuho Toba. She killed Akaza by applying the poison on the back of her spoon when trying the cheese so the poison would get on all but the section of cheese that she tasted. Then she switched out the spoon when she wiped away the dropped cheese on Jisaburou's clothing. She stabbed Moyono with an iron skewer when Moyono's guard was down. She proceeded to stab Jisaburou with two iron skewers connected together to make the wound look like a chisel.
She wrote the letter to Mouri so he could prove her innocence.