MPC and MPS relationship
You are correct in stating that if MPS increases, then MPC decreases.  But the question doesn't actually say that MPS increases. What it says is that saving increases at each level of income. That's consistent with a scenario such as the following in which MPS does not change while autonomous consumption falls from $10$ to $5$:

$\qquad$Before: $S = -10 + 0.2Y$ and $C = 10 + 0.8Y$

$\qquad$After: $S = - 5 + 0.2Y$ and $C = 5 + 0.8Y$

In this scenario, consumption falls by $5$ at each level of income - a parallel shift of the consumption function as per option C.

Actually, the question is not as precisely worded as it could have been.  If C is given as the correct answer, the implication is that households decide to save the same amount more at each level of income.  That could have been made explicit.